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Algebra 1 : Equations of Lines

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Example Questions

Example Question #71 : How To Find Out If Lines Are Parallel

Find a line parallel to the line with the equation:

20y-16x=40

Possible Answers:

$y=\frac{5}{4}x-8$

$y=\frac{4}{5}x+\frac{1}{2}$

y=16x+6

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

Correct answer:

$y=\frac{4}{5}x+\frac{1}{2}$

Explanation:

Lines can be written in the slope-intercept format:

y=mx+b

In this format, equals the line's slope and represents where the line intercepts the y-axis.

First, put the given line in y=mx+b form.

20y-16x=40

We need to isolate on the left side of the equation. Add 16x to both sides of the equation.

20y-16x+16x=40+16x

Simplify.

20y=40+16x

Divide both sides of the equation by .

$\frac{20y}{20}=\frac{40}{20}+\frac{16x}{20}$

Simplify.

$y=2+\frac{16}{20}x$

Reduce.

$y=2+\frac{4}{5}x$

Rearrange terms to match the slope-intercept form.

$y=\frac{4}{5}x+2$

In the given equation:

$m=\frac{4}{5}$

Parallel lines share the same slope.

Only one of the choices has a slope of $\frac{4}{5}$ .

$y=\frac{4}{5}x+\frac{1}{2}$

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Example Question #77 : How To Find Out If Lines Are Parallel

Find a line parallel to the line with the equation:

7y-14x=16

Possible Answers:

$y=\frac{1}{2}x-\frac{12}{17}$

y=-14x+16

y=-2x+4

$y=2x-\frac{4}{7}$

Correct answer:

$y=2x-\frac{4}{7}$

Explanation:

Lines can be written in the slope-intercept format:

y=mx+b

In this format, equals the line's slope and represents where the line intercepts the y-axis.

First, put the given line in y=mx+b form.

7y-14x=16

We need to isolate on the left side of the equation. Add 14x to both sides of the equation.

7y-14x+14x=16+14x

Simplify.

7y=16+14x

Divide both sides of the equation by .

$\frac{7y}{7}=\frac{16}{7}+\frac{14x}{7}$

Simplify.

$y=\frac{16}{7}+2x$

Rearrange terms to match the slope-intercept form.

$y=2x+\frac{16}{7}$

In the given equation:

m=2

Parallel lines share the same slope.

Only one of the choices has a slope of .

$y=2x-\frac{4}{7}$

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Example Question #78 : How To Find Out If Lines Are Parallel

Find a line parallel to the line with the equation:

12y-18x=24

Possible Answers:

y=-18x+24

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

$y=-\frac{3}{2}x+10$

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

Correct answer:

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

Explanation:

Lines can be written in the slope-intercept format:

y=mx+b

In this format, equals the line's slope and represents where the line intercepts the y-axis.

First, put the given line in y=mx+b form.

12y-18x=24

We need to isolate on the left side of the equation. Add 18x to both sides of the equation.

12y-18x+18x=24+18x

Simplify.

12y=24+18x

Divide both sides of the equation by .

$\frac{12y}{12}=\frac{24}{12}+\frac{18x}{12}$

Simplify.

$y=2+\frac{18}{12}x$

Reduce.

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

Rearrange terms to match the slope-intercept form.

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

n the given equation:

$m=\frac{3}{2}$

Parallel lines share the same slope.

Only one of the choices has a slope of $\frac{3}{2}$ .

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

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Example Question #81 : How To Find Out If Lines Are Parallel

Find a line parallel to the line with the equation:

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

Possible Answers:

$y=\frac{1}{2}x+\frac{17}{2}$

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

y=3x+9

$y=2x-\frac{4}{5}$

Correct answer:

$y=\frac{1}{2}x+\frac{17}{2}$

Explanation:

Lines can be written in the slope-intercept format:

y=mx+b

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

$m=\frac{1}{2}$

Parallel lines share the same slope.

Only one of the choices has a slope of $\frac{1}{2}$ .

$y=\frac{1}{2}x+\frac{17}{2}$

Report an Error

Example Question #82 : How To Find Out If Lines Are Parallel

Find a line parallel to the line with the equation:

y=6x+3

Possible Answers:

y=-6x+6

y=6x-14

y=6

$y=\frac{1}{6}x-9$

Correct answer:

y=6x-14

Explanation:

Lines can be written in the slope-intercept format:

y=mx+b

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

m=6

Parallel lines share the same slope.

Only one of the choices has a slope of .

y=6x-14

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Example Question #131 : Parallel Lines

Which of the following lines are parallel to $y=2x+\frac{7}{3}$

Possible Answers:

$y=-2x+\frac{7}{3}$

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

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

y=2x+3

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

Correct answer:

y=2x+3

Explanation:

By definition, lines are parallel if they have the same slope. Given that the reference equation provided is in the y=mx+b form, we can quickly deduce that the slope is $\small 2$ $\small (m=2)$ . Out of the provided options there is only one answer that offers a slope of , therefore that is the correct answer. The y-intercept is not a determinant of lines being parallel or perpendicular.

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Example Question #131 : Parallel Lines

Are the following lines parallel?

y=3x+10000

$\frac{1}{3}y=x+50$

Possible Answers:

Yes

Don't know

Not enough information

Correct answer:

Yes

Explanation:

Parrallel lines, by definition have the same slope, or .

You must get the second equation into y=mx+b form. To do this you need to multiply everything by , the reciprocate of one-third. So:

$3(\frac{1}{3}y=x+50)$

Which simplifies to y=3x+150

because the first and second equation have the same slope, they are parrallel.

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Example Question #132 : Parallel Lines

Which line is parallel to the following line:

y = 4x - 12

Possible Answers:

4y = 16x +24

4y = x - 16

$y = -\frac{1}{4}x + 12$

y = -4x + 9

y = 5x - 12

Correct answer:

4y = 16x +24

Explanation:

Two lines are parellel if they have the same slope. If we look at an equation of a line in slope-intercept form

y = mx + b

we know that m equals the slope. So, in the equation

y = 4x - 12

the slope of the line is 4. So, the answer must also have a slope of 4. If we look at

4y = 16x +24

we must write it in slope-intercept form. To do that, we must get y by itself. We must divide each term by 4. We get

$\frac{4y}{4} = \frac{16x}{4} + \frac{24}{4}$

y = 4x + 6

The slope of this line is 4. Therefore, it is parallel to the original line.

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Example Question #133 : Parallel Lines

Which of the following lines is parallel to h(t) ?

h(t)=14t+156

Possible Answers:

$y=\frac{-1}{14}t+43$

y=14t-989

y=-14t+234

y=144t+156

Correct answer:

y=14t-989

Explanation:

Which of the following lines is parallel to h(t)?

h(t)=14t+156

Parallel lines have equal slope. In h(t), our slope is 14, so we need the other choice with a slope of 14.

Only one other option has a slope of 14, and that is:

y=14t-989

Don't be fooled by lines with the same y-intercept. Slope is all that matters here!

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Example Question #134 : Parallel Lines

Choose the parallel lines.

Possible Answers:

None of these.

y=2x-5

y=3x+5

y=6x+3

y=-6x+3

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

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

y=-5x-3

$y=\frac{1}{5}x-3$

Correct answer:

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

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

Explanation:

Parallel lines have the same slope. If they didn't, the lines would eventually intersect and certainly would not be parallel. The slope is m in y=mx+b form. Since all of these lines are in slope intercept form just select the two that have the same slope.

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

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

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Algebra 1 : Equations of Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #71 : How To Find Out If Lines Are Parallel

Example Question #77 : How To Find Out If Lines Are Parallel

Example Question #78 : How To Find Out If Lines Are Parallel

Example Question #81 : How To Find Out If Lines Are Parallel

Example Question #82 : How To Find Out If Lines Are Parallel

Example Question #131 : Parallel Lines

Example Question #131 : Parallel Lines

Example Question #132 : Parallel Lines

Example Question #133 : Parallel Lines

Example Question #134 : Parallel Lines

All Algebra 1 Resources

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