when an integer is subtracted from 8 times the next consecutive integer, the difference is 71. Find the vale of the greater integer.
Answers
First, define variables for the integer and the next consecutive integer. Then set up an equation that represents the problem. Solve for x. Since x+1 is greater than x, insert your value into the expression and evaluate.
See details:
The value of the greater integer will be 10.
What is linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
The algebraic expression is,
'' An integer is subtracted from 8 times the next consecutive integer, the difference is 71.''
Now,
Let a number = x
Then, Its consecutive number = (x + 1)
So, We can formulate;
⇒ 8 (x + 1) - x = 71
Solve for x as;
⇒ 8x + 8 - x = 71
⇒ 7x + 8 = 71
⇒ 7x = 71 - 8
⇒ 7x = 63
⇒ x = 9
Thus, The value of greater number = x + 1
= 9 + 1
= 10
Therefore, The value of the greater integer will be 10.
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Related Questions
Expand and simplify 3(2x-1) + 2(2x + 5)
Answers
Use the distributive property to expand the binomials.
3(2x - 1) = 6x - 3
2(2x + 5) = 4x + 10
6x - 3 + 4x + 10
Combine like terms.
6x + 4x + 10 - 3
10x + 7
Step-by-step explanation:
3(2x-1)+2(2x+5)
6x-3+4x+10
6x+4x+10-3
10x+7
Select all of the TRUE statements
A.
Dilations of a triangle are congruent to the original triangle.
B.
Dilations always increase the length of line segments.
C.
Dilations of a triangle are similar to the original triangle.
D.
Dilations of perpendicular lines remain perpendicular lines.
E.
Dilations increase the measure of angles.
F.
Dilations of an angle are congruent to the original angle.
Answers
The statements which are true include the following:
C. Dilations of a triangle are similar to the original triangle.
D. Dilations of perpendicular lines remain perpendicular lines.
F. Dilations of an angle are congruent to the original angle.
The types of transformation.In Geometry, there are different types of transformation and these include the following:
ReflectionRotationTranslationDilationWhat is dilation?Dilation simply refers to a type of transformation which changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.
In this context, we can reasonably infer and logically deduce that a dilation of perpendicular lines would always remain perpendicular lines because it takes each of the line to another perpendicular line.
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what is the equivalent ratios of 500:10?
Answers
Step-by-step explanation:
1. Transform by dividing both sides by Highest common factor which is 10 in this case.
2. Final answer is 50:1
veronica went on three hikes. on each hike, she saw the following numbers of animals: hike length of hike (\text{km})(km)left parenthesis, start text, k, m, end text, right parenthesis number of animals seen rivers edge 333 888 wooded marsh 888 242424 canyon creek 151515 353535 veronica tried to order the hikes from least to greatest by number of animals seen per kilometer, but she made a mistake. here's her work: \stackrel{\text{least}}{\underbrace{8} \text{river's edge}} < \underbrace{24} \text{wooded marsh} < \stackrel{\text{greatest}}{\underbrace{35} \text{canyon creek}} river’s edge 8 least < wooded marsh 24 < canyon creek 35 greatest start underbrace, 8, end underbrace, start subscript, start text, r, i, v, e, r, ', s, space, e, d, g, e, end text, end subscript, start superscript, start text, l, e, a, s, t, end text, end superscript, is less than, start underbrace, 24, end underbrace, start subscript, start text, w, o, o, d, e, d, space, m, a, r, s, h, end text, end subscript, is less than, start underbrace, 35, end underbrace, start subscript, start text, c, a, n, y, o, n, space, c, r, e, e, k, end text, end subscript, start superscript, start text, g, r, e, a, t, e, s, t, end text, end superscript what was veronica's mistake? choose 1 answer: choose 1 answer: (choice a) a veronica ordered from greatest to least instead of least to greatest. (choice b) b veronica ordered by number of animals instead of by animals per kilometer. (choice c) c veronica calculated kilometers per animal instead of animals per kilometer. show calculator
Answers
The most appropriate choice for distance will be given by
Veronica has not calculate the number of animals seen per kilometer, she has arranged only on the basis of animals seen.
What is distance?
Distance is how much ground travelled by an object during its motion.
Here,
For River Edge
Number of animals seen = 8
Length of hike = 3 km
Number of Animals seen per km = 8/3
=2.66
For Wooden Marsh
Number of animals seen = 24
Length of hike = 8 km
Number of Animals seen per km = 24/8
=3
For Canyon Creek
Number of animals seen = 35
Length of hike = 15 km
Number of Animals seen per km = 35/15
=2.33
So from least to greatest it will be
Canyon Creek, River Edge, Marshy Land
Veronica has not calculate the number of animals seen per kilometer, she has arranged only on the basis of animals seen. That was her mistake.
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Answer:
B
Step-by-step explanation:
Which answer is an equation in point-slope form for the given point and slope?
Point: (5, 9); Slope: 2
Responses
y−9=2(x−5)
y−5=2(x+9)
y−9=2(x+5)
y+9=2(x−5)
Answers
The equation which forms the correct slope-point form equation is
y - 9 = 2( x - 5). Thus, option (1) is the answer.
The point-slope form is a method that uses the slope of the line and a random coordinate on any point of the line to create an equation of that line.
The equation in the point-slope form is written in the format: [tex]y-y_{1}=m(x-x_{1})[/tex] , where m is the slope and [tex]x_{1}[/tex] and [tex]y_{1}[/tex]are the coordinates of the point on the line.
The given slope is 2, the x-coordinate is 5, and the y-coordinate is 9. There will be no addition symbol in the equation. There is only a subtraction of the coordinates in the equation form. Since options 2, 3, and 4 have addition signs, they do not show the correct equation.
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Which of the following represents the inequality 6x -2 ≥
≥
10
Answers
Answer:
Option 2
Step-by-step explanation:
[tex]6x-2 \geq 10 \\ \\ 6x \geq 12 \\ \\ x \geq 2[/tex]
So, we want a graph with a closed circle at 2 with the arrow pointing to the right.
Answer:
2nd choice
Step-by-step explanation:
6x - 2 ≥ 10
add 2 to both sides
6x - 2 + 2 ≥ 10 + 2
6x ≥ 12
divided b0th sides by 6 to get x alone
6x/6 ≥ 12/6
x ≥ 2
x is greater than or equal to 2
equal to 2 is shown by a shaded in circle (cannot be option 3 or 4)
x is bigger than 2 so the arrow is to the right
Rewrite 72.3 + (-39.1) by breaking up each of the place values. In this case, the place values are tens, ones, and tenths.
Answers
72.3 - 39.1 = 4 tens - 7 ones - 2 tens is the correct order after rewriting.
Given the formula 72.3 + (-39.1)
removing the parentheses:
= 72.3 + (-39.1) (-39.1)
= 72.3 - 39.1
converting decimal numbers to place values
72.3 = 7tens plus 2units plus 3tenths
72.3 = 7(10) (10)
+2(1)+3(1/10)
72.3 =70+2+0.3
Similarly, 39.1
39.1 = 3tens plus 9units plus 1tenth
39.1 = 3(10)+9(1)+1(1/10)
39.1 =30+9+0.1
72.3 - 39.1 = 70+2+0.3 - (30+9+0.1)
72.3 - 39.1 = 70+2+0.3 - 30-9-0.1
72.3 - 39.1 = 70-30+2-9+0.3-0.1
72.3 - 39.1 = 40 - 7 +0.2
Hence after rewriting we get 72.3 - 39.1 = 4 tens - 7 ones - 2 tens
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an amusement park sells child and adult tickets at a ratio of 8:1. on saturday they sold 147 more child tickets than adult tickets. how many tickets did the amusment park sell on saturday?
Answers
4.17. for a standard normal random variable z, compute (a) p(z ≥ 0.99) (b) p(z ≤ −0.99) (c) p(z < 0.99) (d) p(|z| > 0.99) (e) p(z < 10.0) (f) p(z > 10.0) (g) with probability 0.9, variable z is less than what?
Answers
Answer: 1.28
Step-by-step explanation:
1. P(Z > 0.99) = 1 -Ф (0.99) = 1-0.8389 = 0.1611
2.P(Z <-0.99) = Ф(-0.99) = 0.161 (known that from [a] by symmetry)
3.P(Z <0.99) = Ф(0.99) = 0.8389
4. P(Z >0.99) = P(Z <-0.99) + P(Z > 0.99) = 2(0.1611) = 0.3222
The value z = 10.0 is out because it is too large. On comparing with the largest value, z = 3.99,
we get
5. P(Z < 10.0) > P(Z <3.99) = 1.0
6.P(Z > 10.0)<P(Z > 3.99) =10.0
7. On solving the equation
Ф(Z) = 0.9
for Z.
In Table A4, find the value of z corresponding to the probability 0.9. The nearest value is Ф(1.28) = 0.8997. Therefore, z ≈ 1.28
Which numbers are rational?
Answers
The result is -
Rational number: 5/4, -8, 2.35 bar, 19/7, 8, 0Irrational number: πWhat is meant by Rational number?Rational are numbers which can be written with in form p/q, in which q and p are integers and q≠0. is a negative number.
The distinction among rational numbers as well as fractions is that fractions cannot include a negative denominator or numerator. As a result, the numerator and denominator of the a fraction are all numbers (denominator 0), whereas the numerator and denominator of rational numbers are integers.A rational number, p/q, is considered to be in standard form if its numerator and denominator (p and q) share no common divisor (or factor) other than 1 and its denominator "q" is positive.For the given number-
π, 5/4, -8, 2.35 bar, 19/7, 8, 0
All numbers except π are rational as they are either ending number or have the bar which means they will repeat after some point.
π is the only number which have the value 3.14........and so o such that, it is nether terminating nor repeating.
Thus, π is the irrational number.
Therefore, rational numbers are- [5/4, -8, 2.35 bar, 19/7, 8, 0]
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1.2x10^8 x 4.0x10^3
Scientific Notation
Answers
Answer:
4.8x10^11
480000000000
Step-by-step explanation:
Mrs. Walter wanted to plant one daffodil for every 3 tulips in her garden. If she planted 20 daffodils, how many tulips did she plant?
Answers
Answer:
60 tulips
Step-by-step explanation:
1 daffodils : 3 tulips
Since she planted 20 daffodils
20 × 3 = 60 tulips
given six people how many combinations of three are possible if the order does NOT matter
Answers
Answer:
20 Combos
Step-by-step explanation:
6C3 = 6! / ( 3! * 3!) = 20 COMBOS
Is the graph of f(x) = (4/5)^(x) Increasing or Decreasing?
Answers
The graph of the function f(x) = (4/5)^(x) is decreasing.
We are given a graph.The graph shows the function f(x).The function f(x) equals (4/5)^(x).We need to check whether the given function f(x) is increasing or decreasing.f(x) = (4/5)^(x)f(x) = (0.8)^(x)We can see that 0.8 lies between 0 and 1.We know that if a number lies between 0 and 1, it becomes more and more small as it is raised to a higher power.Even from the given graph, we can see that the function is always decreasing as we go from left to right.The function f(x) is an exponentially decreasing function.To learn more about functions, visit :
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Beth owns a coffee shop. She uses half a litre of mayonnaise each day. Mayonnaise costs £2.35 for a 1 litre jar and £4.65 for a 2 litre jar. Beth buys enough mayonnaise to last for 14 days. What is the lowest price Beth can buy this mayonnaise for? Show your working.
Answers
Answer:
£16.30
Step-by-step explanation:
0.5*14=7 litres for 2 weeks
The total cost to buy 7 litres = 7 × 2.35 = 16.45
The cost of 7 litres with the 1 litre jars is £16.45
The total cost to buy 7 litres = (4.65 × 3) + 2.35 = 16.30
The cost of 7 litres with the 2 and 1 litre jars is £16.30
16.45-16.30=15p
The lowest price Beth can buy this mayonnaise for £16.30.
What are arithmetic operations?The study of numbers and their operations, which are crucial to all other fields of mathematics, is included in the field of arithmetic operations. Addition, subtraction, multiplication, and division are the four basic operations of these systems.
It is given that, A coffee business is owned by Beth. Every day, she consumes half a litre of mayonnaise. A 1-litre jar of mayonnaise costs £2.35, and a 2-litre container costs £4.65. Beth purchases 14 days' worth of mayonnaise.
We have to find the cheapest price Beth can get this mayo for,
0.5*14=7 litres for 2 weeks
The total cost to buy 7 litres is,
= 7 × 2.35
= 16.45
The cost of 7 litres with the 1-litre jars is £16.45
The total cost to buy 7 litres is,
= (4.65 × 3) + 2.35
= 16.30
Thus, the cheapest price Beth can buy this mayonnaise for £16.30.
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In the graph of An inequality, the area above a solid line through the point (-5,2) and (3,2) is shaded. Which inequality does this graph represent?
Answers
The inequality shown by this graph is y ≥ 2.
Describe inequality.the relationship between two non-equal expressions using a symbol like "not equal to," ≠ "greater than >," or "less than < "
The inequality sign : ≥ or ≤ to use is: or because the line is solid and not dotted.
Given that the points have y-coordinate values of 2, (-5, 2), and (3, 2), respectively, and that the line crosses the y-axis at this point, the proper inequality is:
y ≥ 2
Therefore, y ≥ 2 is the inequality.
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Jose made this table to show the relationship between his age and his cousin Mario's age.
Jose wants an equation he can use to find his own age (j) given Mario's age (m).
Complete Jose's equation:
y=_____
Thanks so much have a good day!
Answers
The equation that can be used to determine Jose's age given Mario's age is j = [tex]3\frac{1}{3}[/tex]m
What is the equation?Th relationship between Jose's age and Mario's age can be modelled as a linear equation. A linear equation is an equation that when graphed is a straight line. The straight line can either slope upward or downward.
A linear equation is an equation that increases at a constant rate. It has a single variable that is raised to the power of one.
Looking at the table, there is a proportional relationship between Jose's age and Mario's age.
A proportional relationship has this form: j = bm
Where:
j = Jose's age m = Mario's age b = constant of proportionality10 = b3
b = 10 / 3
b = 3 1/3
j = [tex]3\frac{1}{3}[/tex]m
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Answer:
j=m+7
Step-by-step explanation:
auto pistons at wenming chung's plant in shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. from sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows:
Answers
The value of the mean is 155.96mm
Calculation of the mean is:
n=5
Mean= [tex]\frac{\sum fx}{n}[/tex]
Mean=[tex]\frac{156.9+153.2+153.6+157.5+158.6}{5}[/tex]
Mean=779.8/5
Mean=155.96mm
The question was incomplete, the complete question is given below:
Auto pistons at Wenming Chung's plant in shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. from sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows:
Day Mean X(mm) Range R (mm)
1 156.9 4.2
2 153.2 4.6
3 153.6 4.1
4 157.5 4.8
5 158.6 4.7
What is the value of mean in mm, (round your response to 2 decimal places)
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an acorn is falling from 13 feet in the air if it descends 4.8 feet every second write and solve the equation to determine how long it will take for the acorn to be 1 foot above the ground
Answers
It will take 6 seconds for the acorn to be 1 foot above the ground.
What is linear equation?A linear equation is an algebraic equation of the form y=mx + b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) component are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
A typical form linear equation is, for instance, 2x+3y=5. When an equation is provided in this format, finding both intercepts is rather simple (x and y).
Given:
acorn is falling from 13 feet
Every seconds it descends = 4.8 feet
let us assume that the equation for the distance between the acorn from the ground is
x =13 - 4.8 y
where is y is time in seconds and x is the distance
if x = 1 foot
1 = 13 -4.8y
-12 = -4.8y
y = -12 / -4.8
y = 2.5 seconds
Hence, it will take 6 seconds for the acorn to be 1 foot above the ground.
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i am less then 10. i am not a multiple of 2. i am a composite number what am i?
Answers
Answer:
9
Composite numbers under 10:
4,6,8, and 9.
The only one of those 4 that is not a multiple of 2 is 9
Step-by-step explanation:
Hope it helps! =D
Kamryn’s doctor recommended that she drink 64 fluid ounces of water every day. There are about 30 milliliters in 1 fluid ounce. Which measurement represents the number of milliliters in 64 fluid ounces?
help please
Answers
64 fluid ounces is equivalent to 1920 milliliters in measurement.
What is Unit conversion?Conversion of units means to convert between different units of measurement for the same quantity. Their are many different units that can be used to represent the same quantity. Some examples of units are m, cm, litre etc.
Given is Kamryn’s whose doctor recommended that she drink 64 fluid ounces of water every day and are about 30 milliliters in 1 fluid ounce.
A fluid ounce is a unit of capacity equal to one twentieth of a pint (approximately 0.028 litre)
In one fluid ounces → 30 milliliters.
Then, in 64 fluid ounces there will be → 64 x 30 = 1920 milliliters.
Therefore, 64 fluid ounces is equivalent to 1920 milliliters in measurement.
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Devaugh is 14 years older than Sydney. The sum of there she’s is 98 what is Sydney’s age
Answers
Answer:26
Step-by-step explanation:
determine whether each of the following sequences converges or diverges, and justify your answer. if convergent, find the limit of the sequence. (a) cm
Answers
The sequence {(-0.3)ⁿ} converges by oscillation as n increases magnitude of function decreases so it converges
C. The sequence converges by oscillation. It converges to 0.
Here as n increases magnitude of function decreases so it converges.
But at any two consecutive integers function sign changes and it oscillates. Thus it is not monotonic,
the complete question is
Determine whether the following sequence converges or diverges and describe whether it does do so monotonically or by oscillation. Give the limit when the sequence converges.
{(-0.3)ⁿ}
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The sequence diverges monotonically.
B. The sequence converges monotonically. It converges to ____.
C. The sequence converges by oscillation. It converges to ____.
D. The sequence diverges by oscillation.
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a line passes through the point (1,6) and has a slope of 7. Write an equation in point-slope form for this line.
Please answer quickly.
Answers
Answer:
[tex]y-6=7(x-1)[/tex]
Step-by-step explanation:
The equation of a line with slope [tex]m[/tex] and that passes through [tex](x_1, y_1)[/tex] in point-slope form is [tex]y-y_1=m(x-x_1)[/tex].
Eric has 130 coins consisting of Nickels and quarters. The coins combined value comes to $15.90. Find out how many of each coins Eric has.
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Represent the two coins
Let N represents Nickels
Let Q represents quarters
STEP 2: Get the first equation
Equation 1: Eric has 130 coins consisting of quarters and nickels. This is given as:
[tex]N+Q=130------Equation\text{ 1}[/tex]STEP 3: Get the second equation
The total value of all of the coins is $15.90. Each quarter represents .25 and each nickel represents .05, then the second equation is:
[tex]0.25Q+0.05N=15.90------Equation\text{ 2}[/tex]STEP 4: Multiply Equation 2 by 100 to remove the decimals
[tex]\begin{gathered} Equatio\text{ 2}\times100\text{ will give:} \\ 25Q+5N=1590----Equation\text{ 3} \end{gathered}[/tex]STEP 5: Make N the subject of Equation 1
[tex]undefined[/tex]What am I supposed to do here?
Answers
In linear equation, solar system is 0.002 * 10³⁰ more than sun.
What are a definition and an example of a linear equation?
A linear equation with one variable is one that includes just one variable. It has the expression Ax + B = 0, with A and B being any two actual figures and x being an uncertain variable with only one possible value. Such a linear equation in one variable is 9x + 78 = 18.Mass of solar = 1.991 * 10³⁰
Mass of sun = 1.989 * 10³⁰
= 1.991 * 10³⁰ - 1.989 * 10³⁰
= 10³⁰ ( 1.991 - 1.989 )
= 0.002 * 10³⁰
solar system 0.002 * 10³⁰ is more than sun.
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The equation and graph show the cost to rent movies from two different companies. The cost is a function of the number of movies rented. Which description best compares the two functions? Company 1 Company 2 11 m = movies, d= dollars d=3m + 5 There is a higher rate of change at Company 1. It costs more to rent movies from Company 2. There is a higher rate of change at Company 2. Company 1 adds a higher initial fee to the rental cost.
Answers
The equation is d = 3m + 5
What is an equation?
An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign. Solving an equation with variables entails finding which variables' values make the equality true. The variables for which the equation must be solved are also known as unknowns, and the values of the unknowns that fulfill the equality are known as equation solutions. Identity equations and conditional equations are the two types of equations.
The cost function is given by the equation d = 3m + 5
where, d = dollars, m = movies
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3. In your own words, describe what is
happening in lines 9-14 of the poem "the sea
view"
5. How does the shift in mood after line 8 affect
the reader what is your reaction to this poem?
Please Refer to the poem
"The sea view"
Answers
Answer:
Talks about man's brutality
Step-by-step explanation:
It says man spoils Heaven's glorious works with blood, meaning that Earth was perhaps a gift for humans which we ourselves have ruines by engaging in brutal and barbaric acts of war and murder.
The reader is almost instantly brought into reality. The reader is made to feel like the first half of the poem was an illusion and the second half was the real reality. The sudden drop from a heaven-like and fantastical description to a dark and hellish world, makes teh reader uncomftable and almost as if realisation hits the reader and causes them to feel guilty and almost at unease of their own presence
Prove that the measures of the exterior angles of a triangle have a sum of 360°.
Given: <1, <2, and <3 are exterior angles.
Prove: m<1 +m<+m<3 = 360
Answers
Sum of Exterior Angles of Triangle is 360°.
Define Exterior Angle
The angle between any side of a shape and a line that extends from the next side is known as the exterior angle.
Let's Prove: ∠1 + ∠2 + ∠3 = 360°
The angle that is created between one of a triangle's sides and its adjacent extended side is known as the external angle. A triangle has three external angles. Let's learn about the equation for adding a triangle's exterior angles.
From the figure, we can observe that ∠1, ∠2, and ∠3 are the exterior angles of triangle ABC. We know that the sum of all the exterior angles of any polygon is equal to 360°.
Thus, sum of all the exterior angles of a triangle = 360°
Therefore, In triangle ABC the sum of exterior angles,
∠1 + ∠2 + ∠3 = 360°
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write the equation of a line that passes through the point (2,-1) and has a slope of -3
Answers
Finding the equation using slope-intercept form.
[tex]y=-3x+7[/tex]
OR
Finding the equation using point-slope form.
[tex]y-1=-3[/tex] × [tex](x-2)[/tex]
Hope this helps!