The transformation has a horizontal shift right by 4 units and vertical shift upwards by 3 units.
What do you mean by transformation of a function ?
The modification of a graphed function to create a different version of the parent function is known as transformation.
For the given condition :
The function is y = (x - 4)² + 3.
The above function is transformed from the parent function which is y = x².
We know that , the horizontal shift depends on the value of h. The horizontal shift and it is described as:
y = f (x + h)
Then , the graph of function will be shifted to left by h units.
and
y = f (x - h)
Then , the graph of function will be shifted to right by h units.
If we compare both functions i.e., y = (x - 4)² and y = f (x - h), their is a difference of -1 , it meant shift is right by 4 units.
Now , we know that , the vertical shift depends on the value of k. The vertical shift is described as:
y = f(x) + k
Then , the graph of function will be shifted up by k units.
and
y = f(x) - k
Then , the graph of function will be shifted down by k units.
Here , if we compare functions i.e., y = (x - 4)² + 3 and y = y = f(x) - k , we find out that the graph of function will be shifted upwards by 3 units.
Therefore , the transformation has a horizontal shift right by 4 units and vertical shift upwards by 3 units.
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Richey bought a 35-pound bag of dog food on Monday. His dog eats an
average of 3.5 pounds a day. How many pounds will remain in the bag after 8
days? 7 pounds
Answer:
Step-by-step explanation:
//////////////////////////////
Use the rational zeros theorem to list all possible rational zeros of the following.
The given function is:
[tex]g(x)=-25x^3-5x^2-2x-1[/tex]The theorem states that the factors are p/q where p is the factors of the last term (constant term) and q is the factors of the leading coefficient.
Here the leading coefficient is -25 and the constant term is -1.
The factors are listed below:
[tex]\begin{gathered} -25\Rightarrow\pm25,\pm5,\pm1\Rightarrow q \\ -1=\pm1\Rightarrow p \end{gathered}[/tex]So the value of p/q can be the values shown below:
[tex]\frac{p}{q}\Rightarrow\pm\frac{1}{25},\pm\frac{1}{5},\pm1[/tex]Hence the possible zeroes of the given function are:
[tex]\pm\frac{1}{25},\pm\frac{1}{5},\pm1[/tex]
A group is planning a trip to the local amusement park and needs to make sure everyone has a ticket. Up to 8 people can attend the trip, and the tickets cost $17.50 each. This scenario
is modeled by the function y-17.50x where x is the number of people attending and y is the total cost of the trip. Determine the domain and range for this situation.
DOMAIN:
RANGE:
Answer:
8x17.50
Step-by-step explanation:
Please help immediately
What is the equation of the line that passes through Point (6, 0) and has a Slope of -1/2.
I know that it is f(x) = -1/2x + 3 but I need a step by step and clear explanation.
Answer:
[tex]y = - \frac{1}{2} x + 3[/tex]
Step-by-step explanation:
Please see the attached images for the full solution.
Note that when y is replaced with f(x), it is known as a function instead of an equation.
consider the dihedral point group constructed from two generators express a 3d matrix representation for the two generators of the group in the hexagonal basis
the groups generated by two elements of order 2 are K4 and dihedral group.
We are given that G be a finite group with x, y belong to G have two elements of order two.
We have to prove that <x,y> is either abelian or isomorphic to a dihedral group.
<x,y> means the group generated by two elements of order 2.
We know that Zn is a cyclic group and number of elements of order 2 is always odd in number and generated by one element .So , given group is not isomorphic to Zn
But we are given that two elements of order 2 in given group
Therefore, group G can be K4 or dihedral group
Because the groups generated by two elements of order 2 are K4 and dihedral group.
We know that is abelian group of order 4 and every element of K4 is of order 2 except identity element and generated by 2 elements of order 2 and dihedral group can be also generated by two elements of order 2
Hence, <x,y> is isomorphic to K4 or D2.
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a frog is at the bottom of a 25 foot well. each day he climbs up 3 feet, and each night he slips down 2 feet. how many days will it take him to reach the top of the well?
HELP PLEASE!!!!!!!!!!!
What is the dimensions of a rectangle that is 32ft by 8ft after it is dilated by a scale factor of 7/8
Dimensions of rectangle after dilation of scale factor 7/8 will be
[tex] (\frac{7}{2},14), (\frac{-7}{2},14), (\frac{-7}{2},-14), (\frac{7}{2},-14) [/tex]
Dilation of rectangle :-Dilation means the area of any rectangle increases or decreases due to change in it's dimensions but the shape of that rectangle will remain same.
Now Consider the point of dilation as the center of rectangle and assume that the center of given rectangle is at the origin.
As given the length and width of rectangle is 32ft and 8ft respectively.
∴ The Dimensions of rectangle will be (4,16), (-4,16), (-4,-16) and (4,-16).
Now As the rectangle is diluted by the factor of 7/8.
So Now New Dimensions are Calculated by simply multiplying the available dimensions with the scale factor of dilation.
∴ new Dimension after dilation will be
[tex] (4(\frac{7}{8}),16(\frac{7}{8})), (-4(\frac{7}{8}),16(\frac{7}{8})), (-4(\frac{7}{8}),-16(\frac{7}{8})), (4(\frac{7}{8}),-16(\frac{7}{8})) [/tex]
∴ Dimension after dilution will be ;
[tex] (\frac{7}{2},14), (\frac{-7}{2},14), (\frac{-7}{2},-14), (\frac{7}{2},-14) [/tex]
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Find the area of the triangle described below. Round to the nearest hundredth.b = 20, a = 29, c = 21
Solution
We want to find the area of the triangle given te sides
b = 20
a = 29
c = 21
Note: Hero formula for calculating the Area of a Triangle
We will first find S
[tex]\begin{gathered} S=\frac{a+b+c}{2} \\ S=\frac{29+20+21}{2} \\ S=35 \end{gathered}[/tex]To find the Area
[tex]\begin{gathered} Area=\sqrt[]{S(S-a)(S-b)(S-c)} \\ Area=\sqrt[]{35(35-29)(35-20)(35-21)} \\ Area=\sqrt[]{35\times6\times15\times14} \\ Area=\sqrt[]{44100} \\ Area=210 \end{gathered}[/tex]Therefore, the area is
[tex]Area=210[/tex]x/x+2 - 4/x-2 algeriac equation
The solution of the given equation in quadratic form will be; (x^{2} -6x - 8)/(x^{2} -4 )
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
WE have been given an algebric equation as;
x/x+2 - 4/x-2
Solving it;
[tex]\dfrac{x}{x+2 }- \dfrac{4}{x-2}\\\\\\\dfrac{x(x-2)}{x+2 }- \dfrac{4(x+2 )}{x-2}\\\\\\\dfrac{x(x-2)- 4(x+2 )}{(x+2 )(x-2)}\\\\\\\dfrac{x^{2} -2x- 4x - 8}{x^{2} -2^{2} }\\\\\\\dfrac{x^{2} -6x - 8}{x^{2} -4 }[/tex]
Hence, the solution of the given equation in quadratic form will be;
(x^{2} -6x - 8)/(x^{2} -4 )
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does anyone know how to solve and find out the answer? Thank you so much if you help!
Answer:
perpendicular
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - [tex]\frac{2}{3}[/tex] x + 5 ← is in slope- intercept form
with slope m = - [tex]\frac{2}{3}[/tex]
3x - 2y = 4 ( subtract 3x from both sides )
- 2y = - 3x + 4 ( divide through by - 2 )
y = [tex]\frac{3}{2}[/tex] x - 2 ← in slope- intercept form
with slope m = [tex]\frac{3}{2}[/tex]
• Parallel lines have equal slopes.
clearly the slopes are not equal, so not parallel.
• the product of the slopes of perpendicular lines = - 1
- [tex]\frac{2}{3}[/tex] × [tex]\frac{3}{2}[/tex] = - 1
then the lines are perpendicular to each other.
Answer:
The lines are perpendicular.
Step-by-step explanation:
[tex]3x -2y=4[/tex]
Step 1: Add -3x to both sides.
[tex]3x-2y+-3x=4+-3x[/tex]
[tex]-2y=-3x+4[/tex]
Step 2: Divide both sides by -2.
[tex]\frac{-2y}{-2} =\frac{-3x+4}{-2}[/tex]
[tex]y=\frac{3}{2} x-2[/tex]
Finally...
[tex]y=\frac{3}{2} x-2\neq y=-\frac{2}{3} x+5[/tex] so the lines are not parallel.
However, [tex]\frac{3}{2}[/tex] is the opposite reciprocal of [tex]-\frac{2}{3}[/tex], so, the lines are perpendicular.
(You can also try drawing the lines.)
The figure to the right shows a square floor plan with a smaller square area that will accommodate a combination fountain and pool. The floor with the fountain-pool area removed has an area of 432 square meters and a perimeter of 90 meters. Find the dimensions of the floor and the dimensions of the square that will accommodate the fountain and pool
Considering the area and the perimeter of a square, it is found that:
Each length of the large square floor is of 21 meters, and each length of the small square floor is of 3 meters.
What are the area and the perimeter of a square?Supposing a square of side length s, the area and the perimeter are given as follows:
Area: A = s².Perimeter: P = 4s.The area of the figure is given by the subtraction of the area of the large square, of side length x, by the area of the small square, of side length y, hence:
A = x² - y²
x² - y² = 432.
The perimeter of the figure is the perimeter of the square of side length s added to two edges of the smaller square of side length s, hence:
P = 4x + 2y
4x + 2y = 90.
Then the system of equations to find the dimensions is given as follows:
x² - y² = 432.4x + 2y = 90.The solution of this system is given by:
x = 21 m (each length of the large square floor).y = 3 m (each length of the small square floor).Missing informationThe problem is completed by the image given at the end of the answer.
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Erica prepared 13 flower
arrangements after working 2 hours. How many hours did Erica work if she prepared 26 flower arrangements?
Erica worked 4 hours to prepare 26 flower arrangements.
Erica prepared 13 flower arrangements after working 2 hours.
Time Erica took to prepare 1 flower arrangement = 2 / 13 hours.
Therefore time Erica took to prepare 26 flower arrangement = 2/13 x 26 hours.
=4 hours.
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In the designers proposal, they state that the paths EC and DB each measure 100 feet. They also state that the garden will require 140 feet of hedges. Are their numbers reasonable?
We are given a circle whose diamter is 100 feet. To find out if 140 feet of hedges will fit into it given all the oother dimensions, we will have to calculate the lengths of the chords that correspond to the hedges.
First, let us solve for AE.
[tex]\begin{gathered} chord=2r\sin\theta \\ \\ AE=100\sin50 \\ AE=76.6 \end{gathered}[/tex]We used θ = 50 degrees because we know that the measurement of the arc is equal to the measurement of the central angle.
Now, to solve for the length of ED, we need to find out the measurement of the central angle that subtend it.
Segments AD and EC intersect, thus the following equation must be true for the angles that they form and the arcs that they subtend:
[tex]\begin{gathered} m\angle EXA=\frac{1}{2}(m\hat{AE}+m\hat{DC}) \\ \\ 70=\frac{1}{2}(50+m\hat{DC}) \\ \\ 140=(50+m\hat{DC}) \\ \\ 90=m\hat{DC} \end{gathered}[/tex]Again, using the formula for finding the length of a chord, we can now solve for the length of ED.
[tex]\begin{gathered} chord=2r\sin(\theta) \\ \\ ED=100\sin90 \\ ED=100 \end{gathered}[/tex]Finally, we need to calculate the length of BC. But we know that BC = ED because the diameters meet at a 90-degree angle and so the chords that they subtend are all congruent. You may also think of ∠BYC as being vertical to ∠EYD. So BC should be equal to ED either way. BC = 100
So the total length of the hedges is:
[tex]\begin{gathered} AE+ED+BC \\ =76.6+100+100 \\ =276.6ft \end{gathered}[/tex]Therefore, the numbers given by the designers are not reasonable. 140 feet is too short for the hedges.
Use the distributive property to write an equivalent expression.
9(7r−3s+10)
Thanks!
Answer:
63r-27s+90
Step-by-step explanation:
9 times 7 is 63
9 times -3 is -27
9 times 10 is 90
Ayuda es para mañana son similar figures
Answer:
2. x = 2
3. x = 43.2
4. x = 3.6
Step-by-step explanation:
April is arranging place cards for a wedding reception on a table the brides fa
Using the greatest common factor, it is found that the greatest number of cards that she can place in a row is of 14.
How to find the greatest number of cards that she can place in a row?The number of cards for each family is given as follows:
April's family: 154.Groom's family: 140.We want to find a way to distribute them having the same number of cards in each row, hence this is possible finding the greatest common factor (GCF) of the numbers of 154 and 140.
The GCF is found factoring both numbers 154 and 140 simultaneously by prime factors, as follows:
154 - 140|2 (both 154 and 140 are divisible by 2).
77 - 70|7 (both 77 and 70 are divisible by 11).
11 - 7
There are no numbers for which both 11 and 7 are divisible by, hence the greatest number of cards that she can place in a row is:
gcf(154, 140) = 2 x 7 = 14.
Missing information
The complete problem is:
April is arranging place cards for a wedding reception on a table. The bride's family has 154 cards and the groom's family has 140 cards. She wants the arrangements for the two families to have the same number of cards in each row. What is the greatest number of cards that she can place in a row?
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Rewrite 4^-3 x 4 using a single positive exponent.
The term 4^-3 x 4 can be rewritten using a single positive exponent as 1/4^2.
What is positive exponent?The positive exponent serves as the exponents that contain a positive number, it should be noted that the exponent is the degree at the top[ of the given number which is a negative exponents and the question expect us to turn it to a positive exponents after simplification of the given terms which will be simplified below to the simplest expression.
To rewrite the given term so that it can have a positive exponents then it can be expressed as :
=4^-3 x 4
= 4^-2
1/4^2
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2x-6y=-3
Determine if the given ordered pair. (3, 7/2)
satisfies the given equation.
O YES O No
Answer:
No, it doesn't satisfy.
Step-by-step explanation:
2x - 6y = -3
let us post the ordered pair in the equation and solve it
2(3) - 6(7/2) = -3
6 - 21 = -3
-15 = -3 ...... which isn't equal
so we conclude that the given ordered pair doesn't satisfy the equation.
2. The admission fee at a small fair is $2.50 for children and $4.00 for adults. On a certain day, 2400 people enter the fair and $7140 is collected. How many children and how many adults attended?
Given:
a.) The admission fee at a small fair is $2.50 for children and $4.00 for adults.
b.) On a certain day, 2400 people enter the fair and $7140 is collected.
Let,
x = total number of children
y = total number of adults
Let's generate two equations based on the given scenario:
EQUATION 1: Total number of children and adults entered the fair.
[tex]\text{ x + y = }2400[/tex]EQUATION 2: Total money collected from the admission.
[tex]\text{ 2.5x + 4y = }$7140$[/tex]We will be using the substitution method. We get,
[tex]\text{ x + y = }2400[/tex][tex]\text{ y = }2400\text{ - x}[/tex]Substitute to Equation 2:
[tex]\text{ 2.5x + 4y = }$7140$[/tex][tex]\text{ 2.5x + 4(}2400\text{ - x) = }$7140$[/tex][tex]\text{ 2.5x + 9600 - 4x = }$7140$[/tex][tex]\text{ 2.5x - 4x = }$7140$\text{ - 9600 }[/tex][tex]\text{ -1.5x }=\text{ }-2,460[/tex][tex]\text{ }\frac{\text{-1.5x}}{-1.5}\text{ }=\text{ }\frac{-2,460}{-1.5}[/tex][tex]\text{ x }=\text{ }1,640\text{ children}[/tex]Therefore, 1,640 children went to the fair.
For the adults,
x + y = 2400
1,640 + y = 2400
y = 2400 - 1,640
y = 760 adults
In summary: 1,640 children and 760 adults went to the fair.
Find the slope of the line that passes through (2, 12) and (4, 3). Simplify your answer and write it as a proper fraction, improper fraction, or integer.
The slope of the line passing through the coordinates (2, 12) and (4, 3) is -9/2.
Slope is simply expressed as change in y over the change in x.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Given the data in the question;
Point 1( 2, 12 )
x₁ = 2y₁ = 12Point 2( 4,3 )
x₂ = 4y₂ = 3To determine the slope, plug the given x and y values into the slope formula and simplify.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 3 - 12 )/( 4 - 2 )
Slope m = ( -9 )/( 2 )
Slope m = -9/2
Therefore, the slope of the line is -9/2.
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A sculpture is formed from a cylinder resting on top of a cuboid...
The cylinder has radius 40 cm and height 70 cm.
The cuboid measures 80 cm by 80 cm by 140 cm.
The sculpture is made of steel.
The steel has a density of 8.05 g/cm³.
Calculate the total mass of the sculpture in tonnes.
The most appropriate choice for volume of cuboid and cylinder will be given by-
Total mass of sculpture is 10.0464 tonnes
What is volume of cuboid and cylinder?
Cuboid is a three dimensional figure that has 6 faces, 12 edges and 8 vertices.
Volume of cuboid is given by the formula length [tex]\times[/tex] breadth [tex]\times[/tex] height
Cylinder is a three dimensional round figure that has two circular bases at the end
If r is the radius of the cylinder and h is the height of the cylinder, volume of the cylinder is given by the formula
V = [tex]\pi \times r^2 \times h[/tex]
Here,
Radius of cylinder = 40 cm
Height of cylinder = 70 cm
Volume of cylinder = [tex]\pi \times r^2 \times h[/tex]
= [tex]\frac{22}{7} \times (40)^2 \times 70\\[/tex]
= 352000 [tex]cm^3[/tex]
Length of cuboid = 80 cm
Breadth of cuboid = 80 cm
Height of cuboid = 140 m
Volume of cuboid = [tex]80 \times 80 \times 140[/tex]
= 896000 [tex]cm^3[/tex]
Total volume of sculpture = (352000 + 896000) [tex]cm^3[/tex]
= 1248000 [tex]cm^3[/tex]
Density of sculpture = 8.05 [tex]g / cm^3[/tex]
Mass of sculpture = [tex]1248000 \times 8.05[/tex]
= 10046400 g
= 10046.4 kg
= 10.0464 tonnes
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solve the equation for all values of x in simplest form (x+1)^2=15
Answer: [tex]x=-1 \pm \sqrt{15}[/tex]
Step-by-step explanation:
[tex](x+1)^2 =15\\\\x+1 =\pm \sqrt{15}\\\\x=-1 \pm \sqrt{15}[/tex]
Need some help with this, thanks! (And quick thank you! I'd also like an explanation on how these problems get solved , please!)
Answer:
9.38%
Step-by-step explanation:
First this is the solution I used:
Percentage change = actual change/original amount x 100
Hope this helps.
You get paid
$10.75 an hour at your job and the newest video game costs
$60.00 Find the inequality that represents the number of hours you will need to work in order to afford the video game. Use x as a variable
The inequality that represents the number of hours you will need to work in order to afford the video game is x ≥ 5.58.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that two expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤
Let the number of hours be represented as x.
The person is paid $10.75 an hour at your job and the newest video game costs $60.00. This will be illustrated as:
10.75x ≥ 60
Divide
x ≥ 60 / 10.75
x ≥ 5.58
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Please help me out with questions 20.-24.
Answer:
answers are in the photo
Passes to the point( -5, 6) and has a slope equal to 3
Help due tomorrow !!
The equation of a line that passes through the point ( -5, 6) and has a slope equal to 3 is y = 3x + 21
How to find equation of a line using slope?The equation of the line passes through the point (-5, 6) and has a slope equal to 3.
Therefore, the equation of a line can be represented as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore,
y = 3x + b
slope = 3
using (-5, 6), let's find the y-intercept
6 = 3(-5) + b
6 = - 15 + b
b = 6 + 15
b = 21
Therefore, the equation of the line is y = 3x + 21
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Convert repeating decimals to fractions.
Rewrite as a simplified fraction.
3.83 =?
As a fraction 3.83 (3 repeating )is 3x 83/99
what is repeating decimals ?
Repeating decimal values are created by fraction that do not divide evenly. when converting a repeating decimal to a fraction we can ignore the units in the start as the units remain unchanged ,which allows us to convert our decimal values and then the units back in afterward.
so ,
To convert the 3.83 to a fraction , we ignore the units as they will remain units.
we then set up one equation of our unknown x being equal to 0.83333......and another that is 100 times greater , 100x = 83.33333....
by subtracting these two equation from each other we can then divide by the coefficient of x to create our fraction .
10x=83.3333...
x= 0.83333...
99x = 82.5
we now divide both sides by 99 to isolate x:
99x=82.5
99x/99=82.5/99
x= 82.5/99
x = 82.5 x10/99x10
x = 825/990
x = 165/198
we cannot simplify this fraction any more
finally we add back the 3 units we set aside at the beginning ,making our fraction 3x165/198
so , the fraction 3.83 is 3x 83/99
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Select the correct answer from the drop-down menu.The answer choices are in the black box.....which one is it?
ANSWER
C and D
EXPLANATION
Step 1: Given that:
[tex]C\text{ = }\begin{bmatrix}{2} & 1{} & {} \\ {1} & {}2 & {} \\ {2} & {1} & \end{bmatrix}\text{ and D = }\begin{bmatrix}{\sqrt[]{4}} & 1{} & {} \\ {1} & {}\sqrt[]{4} & {} \\ {\sqrt[]{4}} & {1} & \end{bmatrix}[/tex]Step 2: Simplify matrix D
[tex]\begin{gathered} \text{D = }\begin{bmatrix}{\sqrt[]{4}} & 1{} & {} \\ {1} & {}\sqrt[]{4} & {} \\ {\sqrt[]{4}} & {1} & \end{bmatrix}\text{ = }\begin{bmatrix}{2} & 1{} & {} \\ {1} & {}2 & {} \\ {2} & {1} & \end{bmatrix}\text{ since }\sqrt[]{4}\text{ = 2.} \\ \end{gathered}[/tex]Hence, matrices C and D are equal.
True or false
-5/-1 = 5?
(0/-4) = 0?
-3/1 = -3?
- 8/0 = 0?
Checking if the results of the following divisions are true or false.
a) -5/-1 = 5 ↔ True
The fraction, (remembering that it is a division), -5/-1 can be simplified to 5 by removing the negative sign from the numerator and denominator.
b) (0/-4) = 0 ↔ True
We know that any number divided by zero, the result will always be zero.
c) -3/1 = -3 ↔ True
Any number divided by one equals the same number.
d) -8/0 = 0 ↔ False
A normal number simply cannot be divided by 0.
The three previous divisions are true, that is, your answers are correct. While the last one can't, since it can't be divided by 0, this one is false.
Which equation has a graph that is parallel to the graph 2x-y = -1
The equation whose graph is parallel to that of line 2x - y = - 1 is →
y = - 2x - 1
What is the general equation of straight line?
The general equation of straight line is -
y = mx + c
Given is an equation of line as → 2x - y = - 1
The equation of the line whose graph will be parallel to that of the graph of line 2x - y = -1, will have same slope as that of given line itself.
2x - y = - 1
y = -2x - 1
m = -2
The equation whose graph is parallel to that of 2x - y = -1 is -
y = - 2x - 1
Therefore, the equation whose graph is parallel to that of line 2x - y = - 1 is → y = - 2x - 1
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