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Algebra 1 : How to find the equation of a parallel line

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Example Questions

Example Question #1 : How To Find The Equation Of A Parallel Line

Find a line parallel to

y=2x-4

Possible Answers:

y=2x+4

y=-2x+4

y=-2x-4

$y=\frac{1}{2}x+4$

y=2x-4

Correct answer:

y=2x+4

Explanation:

y=2x+4

A parallel line will have the same value, in this case , as the orignal line but will intercept the y-axis at a different location.

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Example Question #2 : How To Find The Equation Of A Parallel Line

Which of the following lines are parallel to the line defined by the equation:

3y=x-2

Possible Answers:

$y=\frac{x}{3}+72$

$y=-3x-\frac{2}{3}$

3y=x-7

y=x-3

3y=2x-2

Correct answer:

$y=\frac{x}{3}+72$

Explanation:

Parallel means the same slope:

3y=x-2

y=mx+b

Solve for :

$y=\frac{x}{3}-\frac{2}{3}$

$m=\frac{1}{3}$

Find the linear equation where

$m=\frac{1}{3}$ .

$y=\frac{x}{3}+72$

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Example Question #1 : Parallel Lines

What is the equation of the line parallel to y=4x+2 that passes through (1,1)?

Possible Answers:

y=4x+3

$y=-\frac{x}{4}-\frac{5}{4}$

y=4x-3

$y=-\frac{x}{4}+\frac{5}{4}$

Correct answer:

y=4x-3

Explanation:

The line parallel to y=4x+2 will have the same slope.

The equation for our parallel line will be: $\ y=4x+b$ .

Using the point (1,1) we can solve for the y-intercept:

1=4(1)+b

$\ 1=4+b$

1-4=b

-3=b

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Example Question #2 : Parallel Lines

Which of these lines is parallel to 4y+2x=6 ?

Possible Answers:

y=4x-1

y=2x-3

$y=-\frac{1}{2}x-4$

y=-2x+5

$y=\frac{1}{2}x-11$

Correct answer:

$y=-\frac{1}{2}x-4$

Explanation:

Parallel lines have identical slopes. If you convert the given equation to the form y=mx+b , it becomes

$y=-\frac{1}{2}x+\frac{3}{2}$

The slope of this equation is $-\frac{1}{2}$ , so its parallel line must also have a slope of $-\frac{1}{2}$ . The only other line with a slope of $-\frac{1}{2}$ is

$y=-\frac{1}{2}x-4$

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Example Question #1 : Parallel Lines

Which of these lines is parallel to

2y-3x=8?

Possible Answers:

$y=\frac{3}{2}x-6$

$y=-\frac{3}{2}x-2$

y=3x+4

None of the other answers are correct.

$y=-\frac{2}{3}x-5$

Correct answer:

$y=\frac{3}{2}x-6$

Explanation:

Parallel lines have identical slopes. To determine the slope of the given line, convert it to y=mx+b form:

2y = 3x + 8

$y=\frac{3}{2}x+4$

This line has a slope of $\frac{3}{2}$ .

The only answer choice with a slope of $\frac{3}{2}$ is $y=\frac{3}{2}x-6$ .

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Example Question #3 : Parallel Lines

Choose which of the four equations listed is parallel to the given equation.

$y=\frac{3}{4}x+7$

Possible Answers:

$2y=\frac{3}{2}x+3$

$y=-\frac{4}{3}x+7$

$y=-\frac{3}{4}x$

$2y=\frac{3}{4}+9$

Correct answer:

$2y=\frac{3}{2}x+3$

Explanation:

$2y=\frac{3}{2}x+3$ is the correct answer because when each term is divided by 2 in order to see the equation in terms of y, the slope of the equation is $\frac{3}{4}$ , which is the same as the slope in the given equation. Parallel lines have the same slope.

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Example Question #5 : Parallel Lines

Write an equation for a line that is parallel to $y=-\frac{1}2{}x+6$ and has a y-intercept of .

Possible Answers:

$y=-5x-\frac{1}{2}$

$y=-\frac{1}{2}x-5$

$y=-\frac{1}{2}x+6$

y=-2x-5

y=2x-5

Correct answer:

$y=-\frac{1}{2}x-5$

Explanation:

The equation of a line can be written using the expression y=mx+b where is the slope and is the y-intercept. When lines are parallel to each other, it means that they have the same slope, so $m=-\frac{1}{2}$ . The y-intercept is given in the problem as . This means that the equation would be $y=-\frac{1}{2}x-5$ .

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Example Question #8 : How To Find The Equation Of A Parallel Line

Write the equation for a line parallel to $\small y=\frac{1}{4}x-5$ passing through the point $\small (4, -2)$ .

Possible Answers:

$\small y=\frac{1}{4}x-3$

$\small y=\frac{3}{4}x-6$

$\small y = \frac{3}{4}x-5$

$\small y=\frac{1}{4}x + 3$

Correct answer:

$\small y=\frac{1}{4}x-3$

Explanation:

In order to approach this problem, we need to be familiar with the slope-intercept equation of a line, $\small y=mx+b$ where m is the slope and b is the y-intercept. The line that our line is supposed to be parallel to is $\small y=\frac{1}{4}x-5$ . Lines that are parallel have the same slope, m, so the slope of our new line is $\small \frac{1}{4}$ . Since we don't know the y-intercept yet, for now we'll write our equation as just:

$\small y=\frac{1}{4}x+b$ . We can solve for b using the point we know the line passes though, $\small (4, -2)$ . We can plug in 4 for x and -2 for y to solve for b:

$\small -2 = \frac{1}{4}*4 + b$ first we'll multiply $\small \frac{1}{4}*4$ to get 1:

$\small \small -2 = 1 + b$ now we can subtract 1 from both sides to solve for b:

$\small -3 = b$

Now we can just go back to our equation and sub in -3 for b:

$\small y = \frac{1}{4}x -3$

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Example Question #9 : How To Find The Equation Of A Parallel Line

Find the equation of a line that is parallel to y=2x+5 and passes through the point (5,5) .

Possible Answers:

$y=2x+\frac{5}{2}$

None of the other answers.

$y=-\frac{1}{2}x-5$

$y=2x-\frac{5}{2}$

A line cannot pass through this point and be parallel to the original line.

Correct answer:

None of the other answers.

Explanation:

Parallel lines have the same slope. So our line should have a slope of 2x. Next we use the point slope formula to find the equation of the line that passes through (5,5) and is parallel to y=2x+5 .

Point slope formula:

$y-y_{1}=m(x-x_{1})$

y-5=2(x-5)

y-5=2x-10

y=2x-5 is the slope of the line parallel to y=2x+5 which passes through (5,5) .

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Example Question #5 : How To Find The Equation Of A Parallel Line

Find the equation of the line parallel to the given criteria: $m=-\frac{3}{2}$ and that passes through the point (2,-5)

Possible Answers:

$y=\frac{2}{3}x-8$

y=x-5

$y=-\frac{2}{3}x-2$

$y=-\frac{3}{2}x-2$

Correct answer:

$y=-\frac{3}{2}x-2$

Explanation:

Parallel lines have the same slope, so the slope of the new line will also have a slope $m=-\frac{3}{2}$

Use point-slope form to find the equation of the new line.

$y-y_{1}=m(x-x_{1})$

Plug in known values and solve.

$y-(-5)=-\frac{3}{2}(x-2)$

$y+5=-\frac{3}{2}x-\frac{-(3)}2{}2$

$y+5=-\frac{3}{2}x+3$

$y=-\frac{3}{2}x+3-5$

$y=-\frac{3}{2}x-2$

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Algebra 1 : How to find the equation of a parallel line

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : How To Find The Equation Of A Parallel Line

Example Question #2 : How To Find The Equation Of A Parallel Line

Example Question #1 : Parallel Lines

Example Question #2 : Parallel Lines

Example Question #1 : Parallel Lines

Example Question #3 : Parallel Lines

Example Question #5 : Parallel Lines

Example Question #8 : How To Find The Equation Of A Parallel Line

Example Question #9 : How To Find The Equation Of A Parallel Line

Example Question #5 : How To Find The Equation Of A Parallel Line

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