The image of the point B ( − 4 , 6 ) under 270° clockwise rotation is point (-6 , -4).
A transformation that revolves a figure around a point is called a rotation. The rotational center is where we refer to it. The shape and dimensions of a figure remain the same while facing in a different direction. You can rotate a figure either clockwise or counterclockwise.
Under a rotation about the origin, the point A ( 5 , − 1 ) is mapped to the point A ' ( 1 , 5 ) is a -
270° clockwise rotation: (x,y) becomes (-y,x)
The image of the point B ( − 4 , 6 ) under this rotation is
(x , y) = (-y , x)
i.e. (-6 , -4)
Assuming that the rotation's center is at (0, 0). Here are the guidelines for rotation:
90° clockwise rotation: (x,y) becomes (y,-x)90° counterclockwise rotation: (x,y) becomes (-y,x)180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)270° clockwise rotation: (x,y) becomes (-y,x)270° counterclockwise rotation: (x,y) becomes (y,-x)Therefore , The image of the point B ( 4, 6) when rotated 270 degrees clockwise is point (-6 , -4).
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哈!
Natalie used 2 1/2 tubes of blue paint to
paint the sky in her picture. Each tube
holds 4/5 ounces of paint. How many
ounces of blue paint did Natalie use?
Expert hel
me Give example of 6 types of factoring polynomials with Solution
Answer:
1 Greatest Common Factor
We have to find out the greatest common factor, of the given polynomial to factorise it. This process is nothing but a type of reverse procedure of distributive law.
2. Grouping
This method is also said to be factoring by pairs. Here, the given polynomial is distributed in pairs or grouped in pairs to find the zeros.
3. Using Identities
The factorisation can be done also by using algebraic identities. The most common identities used in terms of the factorisation are:
(a + b)2 = a2 + 2ab + b2
(a – b)2 = a2 – 2ab + b2
a2 – b2= (a + b)(a – b)
4. Zero Factor Property :The Zero Factor Property (also called the Zero Product Property) says that if the product of two quantities is zero, then at least one of those quantities is zero. The only way to get a product equal to zero is to multiply by zero itself.
5. Greatest Common Factor (GCF) Method:
This is almost always the first method applied to factoring polynomials. Look at all of the terms and see if they all have something in common that can be removed.
6. Sum or Difference in Two Cubes
A cube is a term that has been multiplied by itself twice.
[tex] {3}^{3} {x}^{3} and \: \: \: {27x}^{3} [/tex]
are all cubed terms. The trick to remembering how to factor cubed terms is S.O.A.P. S = same sign, O = opposite sign A.P. = always positive.
LET f(x)=4x+1 and g(x)=x²-5 (find (f+g) (x)
The function operation ( f + g )(x) of the functions f( x ) = 4x + 1 and g( x ) = x² - 5 is x² + 4x - 4.
What is the function operation ( f + g )(x) in the function?A function is simply a relationship that maps one input to one output.
Each x-values must have one y-value to qualify as a function.
Given the data in the question;
f( x ) = 4x + 1g( x ) = x² - 5( f + g )(x) = ?First, set up the function operation
( f + g )(x) = f(x) + g(x)
Replace the function designators f(x) and g(x) with the actual functions.
( f + g )(x) = f(x) + g(x)
( f + g )(x) = ( 4x + 1 ) + ( x² - 5 )
Collect and add like terms
( f + g )(x) = 4x + 1 + x² - 5
( f + g )(x) = 4x + x² - 5 + 1
( f + g )(x) = 4x + x² - 4
Reorder the function
( f + g )(x) = x² + 4x - 4
Therefore, the function operation ( f + g )(x) is x² + 4x - 4.
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f(-3) = -1, f(-2) = 4
Answer:
1(-3) = -3, 1f(-2) = -2
Step-by-step explanation:
Identify the correct description of the values in both the domain and range of the function
Domain is number of minutes water has been added .
Range is amount in the pond
What are domain and range ?The domain and range of a relation are, respectively, the sets of all the x-coordinates and all the y-coordinates of ordered pairs. For example, if the relationship is R = (1, 2), (2, 2), (3,), (4, 3), then
Domain is the set of all x-coordinates that is all with values of 1, 2, 3, and 4.
The set of all y-coordinates in the range is equal to 2, 3.
Domain : Let y = f(x) be a function with an independent variable x and a dependent variable y.
Range : a function represents a defined relationship between an independent variable (x) and a dependent variable (y). The formula to find the range of a function is y = f(x).
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help me answer this.
Solution:
The cube is numbered from 1 to 6
[tex](S)=6[/tex]The probability that any of the numbers from 1 to 6 will show will be
[tex]Pr(R)=\frac{1}{6}[/tex]The expected value will be calculated below as
[tex]E.V=xP(x)[/tex][tex]undefined[/tex]
A number, n, is multiplied by 5/8 The product is -0.4. What
is the value of n?
Answer:
n= -16/25
Step-by-step explanation:
A unicycle wheel has a diameter of 24 inches.
Image_3150
If the wheel revolves 3 times clockwise, approximately how far does the unicycle travel? (Use 3.14 for π.)
The distance travelled by the unicycle is 226.08 inches.
What is the distance travelled?The first step is to determine the circumference of the wheel of the unicycle. A circle is a bounded figure which points from its center to its circumference is equidistant. The circumference of a circle is the distance round the circle.
Circumference of a circle = 2πr
Where:
π = pi = 3.14 r = radius = diameter / 2 = 24 / 2 = 12 inches3.14 x 2 x 12 = 75.36 inches
The next step is to multiply the circumference of the unicycle by the number of revolutions the tire made.
Distance travelled = 3 x 75.36 inches = 226.08 inches
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Find the measure of each angle indicated
Answer:
68°
Step-by-step explanation:
Alternate exterior angles have the same measurement.
850' of #2 wire is sent to your job. On Monday, you cut 3 pieces, each 175' long. On Tuesday, you cut 3 pieces, each 88' long, and 3 pieces, each 20' long. How much wire is left on the reel?
The remaining wire (W) is just the original wire (850') minus the cut wire on Monday, Tuesday...
[tex]W=850^{\prime}-3\cdot175^{\prime}-3\cdot88^{\prime}-3\cdot20^{\prime}=1^{\prime}[/tex]There is merely 1' of wire in the reel.
Choose all the expressions that are equal to 5/9 × 8
A.
[tex]\frac{9}{5\cdot8}=\frac{9}{40}\ne\frac{40}{9}[/tex]This is not a correct choice
--------------------------
B.
[tex]\frac{8}{9}\times5=\frac{40}{9}[/tex]This is a correct choice
---------------------------
C.
[tex]\frac{5}{8\times9}=\frac{5}{72}\ne\frac{40}{9}[/tex]This is not a correct choice
------------------------------------------------
D.
[tex]5\times\frac{1}{9}\times8=\frac{40}{9}[/tex]This is a correct choice
-------------------------------------------
E.
[tex]\frac{5\times8}{9}=\frac{40}{9}[/tex]This is a correct choice
The lifespans of gorillas in a particular zoo are normally distributed. The average gorilla lives 20.8 years; the standard deviation is 3.1 years.
Use the empirical rule (68 - 95 - 99.7%) to estimate the probability of a gorilla living longer than 23.9 years
The probability of a gorilla living less than 23.9 years is 0.84 (84%) if the lifespans of gorillas in a particular zoo are normally distributed.
How does probability work?A probability is also called as a numerical representation of the likelihood or chance that any kind of specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities. Probability refers to potential.
Any random event's occurrence is the exact subject of this area of mathematics. The range of the value varies from 0 to 1. Mathematics has been incorporated probability to forecast the likelihood of various types of events.
How is probability determined?The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas.
We need to find the z-score herein of 23.9 years in the kind of standard normal distribution of the lifespans of gorillas in this particular zoo.
z score can be further be calculated using the equation
z = (X-M)/s
and it has been given that X is 23.9 years
M is also called the average gorilla life (20.8 years)
s is given as the standard deviation (3.1 years)
Thus, putting up the values, we have
Z = 1
The Empirical rule that is present here states that 68% of the total lifespans lie within 1 standard deviation from the other mean.
Then Half of it, 68/2 = 34 % lies right side of 1 standard span of the mean.
Since this lifespan is less than mean is 50%, 50%+34% =84% lies less than total z-score 1, that is the probability of a gorilla living less than 23.9 years.
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The sum of the forth and thirteen terms of an arithmetic progression is 80. find the sum of the first sixteen terms.
The most appropriate choice for Arithmetic Progression will be given by-
The sum of the first sixteen terms of the Arithmetic Progression is 640
What is Arithmetic Progression?
A series of numbers are said to be in Arithmetic Progression if the difference between consecutive terms of the series are same.
If [tex]a_n[/tex] is the [tex]n^{th}[/tex] term of the series, a be the first term and d the common difference,
[tex]a_n = a+(n-1)d[/tex]
If [tex]S_n[/tex] is the sum of first n terms of the series,
[tex]S_n = \frac{n}{2}(2a+(n-1)d)[/tex]
Here,
Let the first term be a and the common difference be d
The sum of the fourth and thirteen terms of an arithmetic progression is 80.
[tex]a_4 + a_{13} = 80[/tex]
[tex]a + (4-1)d + a + (13-1)d = 80[/tex]
[tex]a + 3d +a +12d =80\\2a+15d =80[/tex]
[tex]S_{16} = \frac{16}{2}(2 \times a + (16 -1) \times d)\\[/tex]
[tex]= 8(2a+15d)[/tex]
[tex]= 8 \times 80[/tex]
[tex]= 640[/tex]
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Why is it important the order we write the vertices of a triangle in a congruent statement? SELECT ALL THAT APPLY!
A The middle letter is the vertex of the angle.
B The order tells us what sides are congruent.
C The order does not matter
D The order tells us what angles are congruent.
It is important the order we write the vertices of a triangle in a congruent statement as
B. The order tells us what sides are congruent.
D. The order tells us what angles are congruent.
How to illustrate the information?A vertex (plural vertices) in geometry is the intersection of two straight lines. Three line segments come together to form a triangle. The ends of a triangle's three sides meet at three separate points in a plane to form the triangle, which has three sides with two endpoints each. The vertices of a triangle are the three distinct intersecting points or corners.
Congruent triangles are triangles that are precisely the same size and shape. The word congruent has the sign. When the three sides and three angles of one triangle match the same dimensions as the three sides and three angles of another triangle, two triangles are said to be congruent.
The vertices of a triangle in a congruent statement are important for the ordering. In conclusion, the correct options are B and D.
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Evaluate a³ - b + 7, if a = 3 and b
=4
⇒Plug in the given values of the variables in order and then simplify the expression
Given that a= 3 and b=4
⇒[tex]=(3)^{3} -(4)+7\\=27-4+7\\=23+7\\=30[/tex]
⇒The expression evaluated at the given known variables gives 30.
At which values of x does the graph of the function F(x) have a vertical asymptote? Check all that apply
Solution
Step 1:
Write the rational expression:
[tex]\begin{gathered} f(x)\text{ = }\frac{x+4}{x^2+5x-24} \\ \end{gathered}[/tex]Step 2:
Vertical asymptotes can be found by solving the equation n(x) = 0 where n(x) is the denominator of the function ( note: this only applies if the numerator t(x) is not zero for the same x value).
Step 3
[tex]\begin{gathered} x^2+5x-24=0 \\ \\ x^2+8x\text{ - 3x - 24 = 0} \\ \\ x(x\text{ + 8\rparen-3\lparen x + 8\rparen = 0} \\ \\ (x\text{ - 3\rparen\lparen x + 8\rparen = 0} \\ \\ x\text{ - 3 = 0, x + 8 = 0} \\ x\text{ = 3, x = -8} \end{gathered}[/tex]Step 4:
\ertical} Asymptote is =-8,\ =3,
A store has 18 cell phones in stock. The manufacturer ships cell phones to the store to sell in boxes that contain four cell phones each. If the store is preparing for a big sale and would like to have 30 cell phones in stock for the sale, how many boxes should they order from the manufacturer?
A. 3
B. 4
C. 8
D. 12
Answer:
The answer is A, 3
Answer:
4 is the answer
How to get the equation of a parabola with 3 pointsy- intercept : (0, -1.4)x-intercept : (0.905,0)3rd point: (2,0.6)
he standard form of a quadratic efunctionis:
[tex]\begin{gathered} y=ax^2+bx+c \\ \text{Where } \\ a,b,\text{ and }c\text{ are real constants such that }a\ne0. \end{gathered}[/tex]Since the y-intercept is (0, -1.4), it follows that:
[tex]\begin{gathered} -1.4=a(0)^2+b(0)+c \\ \text{ Therefore,} \\ c=-1.4 \end{gathered}[/tex]Substitute c = -1.4 into the equation:
[tex]y=ax^2+bx-1.4[/tex]Since the x-intercept is (0.905, 0), it follows that:
[tex]\begin{gathered} a(0.905)^2+b(0.905)-1.4=0 \\ \text{Therefore,} \\ 0.819025a+0.905b=1.4-------(1) \end{gathered}[/tex]Since the graph passes through the third point (2, 0.6), it follows that:
[tex]\begin{gathered} 0.6=a(2)^2+b(2)-1.4 \\ \text{Therefore} \\ 4a+2b-1.4=0.6 \\ 4a+2b=0.6+1.4_{} \\ 4a+2b=2 \\ \text{Divide both sides by }2 \\ 2a+b=1 \\ \text{Hence} \\ b=1-2a---------(2) \end{gathered}[/tex]Substitute equation (2) into equation (1):
[tex]\begin{gathered} 0.819025a+0.905(1-2a)=1.4 \\ 0.819025a+0.905-1.81a=1.4 \\ \text{ Collect like terms:} \\ 0.819025a-1.81a=1.4-0.905 \\ -0.990975a=0.495 \\ \text{ Therefore,} \\ a=\frac{0.495}{-0.990975} \\ a\approx-0.5 \end{gathered}[/tex]Substitute a = -0.5 into equation (2), therefore,
[tex]b=1-2(-0.5)=1+1=2[/tex]Therfore the function is given by:
[tex]y=-0.5x^2+2x-1.4[/tex]The equation of the parabola is y = -0.5x² + 2x - 1.4
.
In triangle ABC, angle B is one-quarter of angle A and angle C is two fifth of angle A. If the size of angle A is (x- 10)°. Form an equation in x and hence calculate the angle of triangle ABC to the nearest degree.
When in triangle ABC, angle B is one quarter off angle B and angle C is two fifth of angle A and the angle A is (x-10) degrees, then the ∠A, ∠B and ∠C are 109 degrees, 27 degrees and 44 degrees respectively
The ∠A = (x-10) degrees
Angle B is one-quarter of angle A
∠B = (1/4)×(x-10)
= (1/4)x - (5/2)
= 0.25x-2.5
The angle C is two fifth of angle A
∠C = (2/5)(x-10)
= (2/5)x - 4
= 0.4x-4
We know sum of the angles in a triangle is 180 degrees
Then,
∠A + ∠B + ∠C = 180
Substitute the values in the equation
(x-10) + 0.25x-2.5 +0.4x-4 = 180
1.65x-16.5 = 180
1.65x = 196.5
x ≈ 119
∠A = (x-10)
= 119-10
= 109 degrees
∠B = 0.25x-2.5
= 0.25×119-2.5
≈ 27 degrees
∠C = 0.4x-4
= 0.4×119-4
≈ 44 degrees
Hence, when in triangle ABC, angle B is one quarter off angle B and angle C is two fifth of angle A and the angle A is (x-10) degrees, then the ∠A, ∠B and ∠C are 109 degrees, 27 degrees and 44 degrees respectively
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What amount of sales will produce a commission of $102.00 if the commission rate is 8.5%?
You would need sales of $[
What is the distance between the points A(-1,3) and point B(-8,3)?
Zoe is making a rectangular box with measurements as shown below 5 inches 3 inches 3 inches what is the surface area of the box
Surface area of rectangular box is 78 inches².
What is surface area?The surface area of an object is the sum of the areas of all of its faces, or the exterior surfaces of its three dimensions. It is calculated in square units. The total area of all faces (or surfaces) on a 3D form is the surface area. The six rectangular faces of a cuboid. Add the areas of each of the cuboid's six faces to determine its surface area. Additionally, we can label the prism's length (l), width (w), and height (h), and then calculate its surface area using the formula SA=2lw+2lh+2hw.
Given Data
rectangular box with measurements as shown below 5 inches 3 inches 3 inches
Length = 5 inches
Width = 3 inches
Height = 3 inches
Surface area formula
2lw + 2lh+2hw
Equating values
2(5)(3) + 2(5)(3) +2(3)(3)
30 + 30 + 18
78
Surface area of rectangular box is 78 inches².
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Evaluate the expression shown below and write your answer as a fraction in simplest form.
\frac{1}{10}+\frac{11}{20}
10
1
+
20
11
The addition of the fraction 1/10 + 11/20 based on the computation will be 13/20.
What is a fraction?In mathematics, a fraction is defined as a portion of the whole. If a pizza is cut into four equal pieces, each slice is represented by ¼.
It should be noted that a fraction simply means a part of a whole number. It should be noted that it's usually expressed as a/b where a is the numerator and b is the denominator.
In this case, we want to add 1/10 + 11/20. This will be illustrated thus:
= 1/10 + 11/20
= 2/20 + 11/20
= 13/20
Therefore the addition is 13/20.
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To measure the height of a building, a person stands away from the base and measures the angle of elevation to the top of the building to be 48∘. Moving 170 feet closer, the angle of elevation to the top of the building is 73∘. How tall is the building?
The height of the building is 118. 89 feet
What are trigonometric identities?Trigonometric identities are simplify defined as arithmetic expressions or equations relating to many trigonometric functions, and is also known for holding true for all the values in the domain of the functions.
The different types of trigonometric identities includes;
sinecosinetangentcotangentsecantcosecantThe trigonometric ratios for major identities are;
sine = opposite/hypotenuse
tangent = opposite/adjacent
cosine = adjacent/hypotenuse
From the information given;
cos 43 = x/170
cross multiply
x = cos 43(170)
expand the bracket
x = 124.33 feet
To determine the height of the building is the opposite side
sin 73 = x/ 124.33
cross multiply
x = sin 73(124.33)
expand the bracket
x = 118. 89 feet
Hence, the value is 118. 89 feet
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g(x)=3x evaluate the function when x=-2, 0, 5
The function g(x) when x= - 2, 0 , 5 is -6 , 0 and 15 respectively.
What are functions?
The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given: g(x) = 3x
To evaluate : The function x= - 2, 0, 5.
g(-2) = 3× -2 = -6
g(0) = 3×0 = 0
g(5)= 3×5 = 15
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what is the y-intercept for the exponential function graphed below
Based on the attached graph, the y-intercept is 3
What is the y-intercept of the function?The y-intercept of the function is the point or points where the graph of the function crosses the y-axis i.e. the point where the value of x equals 0
How to determine the y-intercept for the graph of the exponential function?The graph that completes the question is added as an attachment
Using the definition above, we understand that
The y-intercept for the graph of the exponential function is the point where x = 0
On the attached graph, we have
y = 3, when x = 0
This means that the y-intercept for the graph of the exponential function is 3
This is so because the graph of the function crosses the y-axis at y = 3 when x = 0
Hence, the y-intercept of the exponential function is 3
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Please help me solve question
In this problem, we are looking for the doubling time of the wage of the Toyota automobile assembly line workers. Initially, their wage is $6.70 and by the end of 15 years, their salary is now $29.59.
What we can find here first is the rate of the increase of the salary of the workers. We can use the equation
[tex]y=y_0e^{rt}[/tex]We are looking for the value of r. We have to derive an equation solving for r. We have
[tex]\begin{gathered} \frac{y}{y_0^{}}=e^{rt} \\ rt=\ln \frac{y}{y_0} \\ r=\frac{1}{t}\ln \frac{y}{y_0} \end{gathered}[/tex]Now, we solve for the value of r given y = 29.59, y0 = 6.70, and t = 15 years. We get
[tex]\begin{gathered} r=\frac{1}{15}\ln (\frac{29.59}{6.70}) \\ r=0.099yr^{-1} \end{gathered}[/tex]The doubling time is computed as
[tex]d=\frac{\ln 2}{r}[/tex]Substitute the value of r on the equation above and solve, we get
[tex]d=\frac{\ln 2}{0.099}=7.00yr[/tex]Hence, the doubling time for this problem is equal to 7 years.
Answer: 7 years
the total consumption of fruit juice in a particular country in 2006 was about 2.28 times 10 squared 9 gallons. The population of that country that year was 3 times 10 squares 8 what was the average number of gallons consumed per person in the country 2006
The average consumption of the fruit juice would be 7.6 gallons for the year 2006.
What do you understand by average consumption?Average consumption is derived by dividing the total measured consumption of that municipal service by that consumer during the three months before by three. It refers to the average consumption of a consumer of a municipal service during a certain time.
How is the average consumption determined?Utilizing the total of quantities consumed or dispersed over a period of time, typically 12 months, the average monthly consumption can be computed. The average number of units used each month is known as average monthly consumption, stock-outs corrected (CA).
Total consumption of the fruit juice in 2006=2.28x109 gallons.
Total population of the country in year 2006=3x108
Average Consumption=(2.28x109)/(3x108)
= 7.6 gallons
Hence the average consumption would be 7.6 gallons per person.
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Rewrite the set T by listing its elements. Make sure to use the appropriate set notation.
T= {x|x is an integer and -5
The set T can be rewritten by listing its elements as T = {-4}.
What are sets?A set is a grouping of unique components that are denoted by curly brackets and commas.The term "elements of a set" refer to the collection of items in a set. A collection of fruits or a collection of images are two examples. Sets are additionally shown as follows.Set A = {a, b, c, d}. These are the elements of set A: a, b, c, and d.
Given:
Set T is equal to {x | x is an integer and -5 < x < -3}.
By examining the interval in the set, the set can also be written as something else.
It should be noted that the interval consists of two inequalities combined so that x > -5 and x < -3.
As -4 > -5 and -4 < -3 via the number line so it is the only element listed in the required set notation.
Hence, the set can be rewritten as
T = {-4}
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The complete question is: "Rewrite the set T by listing its elements. Make sure to use the appropriate set notation.
T = {x | x is an integer and -5 < x < -3}."
Find the slope and the y-intercept of the line with the equation 9y - 6x + 8 = 0.Select the correct choice below and fill in any answer boxes within your choice. A. The slope is(Type an integer or a simplified fraction.)B. The slope is undefined.Select the correct choice below and fill in any answer boxes within your choice.A. The y-intercept is(Type an integer or a simplified fraction. Type an ordered pair.)B. There is no y intercept
Rewrite the given equation in slope intercept form, y=mx+c. Where the slope is m and the y-intercept is c.
Rewrite the given equation as follows:
[tex]\begin{gathered} 9y-6x+8=0 \\ \text{Take x term and the constant to the right side and change their sign} \\ 9y=6x-8 \\ \text{Divide each term by 9:} \\ \frac{9y}{9}=\frac{6x}{9}-\frac{8}{9} \end{gathered}[/tex]Simplify the equation:
[tex]y=\frac{6}{9}x-\frac{8}{9}[/tex]Compare to the equation y=mx+c, to get:
[tex]\begin{gathered} m=\frac{6}{9} \\ c=-\frac{8}{9} \end{gathered}[/tex]Hence, the slope is 6/9 and the y-intercept is -8/9.
You can also write the y-intercept as an ordered pair (0,-8/9) since the x-value at the y-intercept is zero.