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ACT Math : How to find the equation of a parallel line

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Example Questions

Example Question #21 : Lines

Which of the following is the equation of a line parallel to the line given by the equation:
y = -4x + -5

Possible Answers:

t = 4x + 3

y = -4x + 6

y = -4x + -5

$y = -\frac{1}{4}x + 5$

$y = \frac{1}{4}x +5$

Correct answer:

y = -4x + 6

Explanation:

Parallel lines have the same slope and different y-intercepts. If their y-intercepts and slopes are the same they are the same line, and therefore not parallel. Thus the only one that fits the description is:

y = -4x + 6

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Example Question #22 : Algebra

A line passes through (4, 2) and (13, 8) . Give the equation, in slope-intercept form, of a parallel line that passes through (-2, 4) .

Possible Answers:

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

$y=\frac{2}{3}x + \frac{16}{3}$

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

$y=-\frac{2}{3}x-\frac{11}{3}$

Correct answer:

$y=\frac{2}{3}x + \frac{16}{3}$

Explanation:

The first step in solving for a parallel line is to find the slope of the original line. In this case, $m=\frac{(8-2)}{(13-4)} = \frac{6}{9} = \frac{2}{3}$ .

Our new line has an equal slope (the definition of parallel) and passes through (-2, 4) , so substituting into our slope-intercept equation gives us:

y=mx+b ---> $4=\frac{2}{3}(-2) +b$ ---> $\frac{12}{3} + \frac{4}{3} = b = \frac{16}{3}$ .

Thus, the slope intercept equation for our parallel line is $y=\frac{2}{3}x + \frac{16}{3}$ .

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Example Question #31 : Coordinate Plane

What is the equation of the line passing through (0,0) and which is parallel to $y=\frac{1}{3}x+7$ ?

Possible Answers:

$y=\frac{1}{3}x-7$

$y=\frac{7}{3}x +1$

$\textup{There is not enough information to give an answer.}$

$y=\frac{1}{3}x$

Correct answer:

$y=\frac{1}{3}x$

Explanation:

Ordinarily, we would use point-slope form, y-y_1=m(x-x_1) , to construct a proper parallel from a point and a slope. However, in this case, we have been given a y-intercept by the problem itself, so sticking with slope-intercept form is easiest.

If the new line passes through (0,0) , then we know the y-intercept is b=0 . Since slope is equal in parallel lines, and the slope of our comparison line is $m=\frac{1}{3}$ , we know the slope of our new line is $m=\frac{1}{3}$ .

Thus, $y=mx+b = \frac{1}{3}x +0 = \frac{1}{3}x$ .

The correct answer is, $y=\frac{1}{3}x$ .

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Example Question #11 : How To Find The Equation Of A Parallel Line

Which of the following equations represents a line that is parallel to the line represented by the equation 10x-4y=26 ?

Possible Answers:

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

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

y=5x-1

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

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

Correct answer:

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

Explanation:

Lines are parallel when their slopes are the same.

First, we need to place the given equation in the slope-intercept form.

10x-4y=26

Subtract 10x from both sides of the equation.

10x-10x-4y=26-10x

Simplify.

-4y=-10+26

Divide both sides of the equation by .

$\frac{-4y}{-4}=\frac{-10}{-4}+\frac{26}{-4}$

Simplify.

$y=\frac{10}{4}x-\frac{26}{4}$

Reduce.

$y=\frac{5}{2}x-\frac{13}{2}$

Because the given line has the slope of $\frac{5}{2}$ , the line parallel to it must also have the same slope.

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

If the line through the points (5, –3) and (–2, p) is parallel to the line y = –2x – 3, what is the value of p ?

Possible Answers:

–10

–17

Correct answer:

Explanation:

Since the lines are parallel, the slopes must be the same. Therefore, (p+3) divided by (–2–5) must equal –2. 11 is the only choice that makes that equation true. This can be solved by setting up the equation and solving for p, or by plugging in the other answer choices for p.

$\frac{p--3}{-2-5}=\frac{p+3}{-2-5}=-2$

$\frac{p+3}{-7}=-2$

$(\frac{p+3}{-7})-7=-2(-7)$

p+3=14

p=11

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ACT Math : How to find the equation of a parallel line

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #21 : Lines

Example Question #22 : Algebra

Example Question #31 : Coordinate Plane

Example Question #11 : How To Find The Equation Of A Parallel Line

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

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