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Algebra 1 : Equations of Lines

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #3991 : Algebra 1

Find the slope of a line parallel to the line with the equation:

$y=\frac{5}{6}x-12$

Possible Answers:

$-\frac{5}{6}$

$\frac{5}{6}$

$\frac{6}{5}$

Correct answer:

$\frac{5}{6}$

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:

$y=\frac{5}{6}x-12$

And it has a slope of:

$m=\frac{5}{6}$

Parallel lines share the same slope.

The parallel line has a slope of $\frac{5}{6}$ .

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Example Question #3992 : Algebra 1

Find the slope of a line parallel to the line with the equation:

$y=\frac{2}{11}x-\frac{1}{4}$

Possible Answers:

$-\frac{2}{11}$

$\frac{2}{11}$

$\frac{11}{2}$

Correct answer:

$\frac{2}{11}$

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:

$y=\frac{2}{11}x-\frac{1}{4}$

And it has a slope of:

$m=\frac{2}{11}$

Parallel lines share the same slope.

The parallel line has a slope of $\frac{2}{11}$ .

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Example Question #3993 : Algebra 1

Find the slope of a line parallel to the line with the equation:

$y=-\frac{8}{13}x+10$

Possible Answers:

$-\frac{8}{13}$

$\frac{13}{8}$

$-\frac{13}{8}$

$\frac{8}{13}$

Correct answer:

$-\frac{8}{13}$

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:

$y=-\frac{8}{13}x+10$

And it has a slope of:

$m=-\frac{8}{13}$

Parallel lines share the same slope.

The parallel line has a slope of $-\frac{8}{13}$ .

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Example Question #3994 : Algebra 1

Find the slope of a line parallel to the line with the equation:

$y=\frac{12}{17}x-123$

Possible Answers:

$\frac{12}{17}$

$\frac{17}{12}$

$-\frac{12}{17}$

123

Correct answer:

$\frac{12}{17}$

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:

$y=\frac{12}{17}x-123$

And it has a slope of:

$m=\frac{12}{17}$

Parallel lines share the same slope.

The parallel line has a slope of $\frac{12}{17}$ .

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Example Question #3995 : Algebra 1

Find the slope of a line parallel to the line with the equation:

y=-12x-12

Possible Answers:

$\frac{1}{12}$

Correct answer:

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:

y=-12x-12

And it has a slope of:

m=-12

Parallel lines share the same slope.

The parallel line has a slope of .

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Example Question #3996 : Algebra 1

If line X is parallel to line A with a slope of $\frac{7}{2}$ and a y-intercept of , what is the slope of line X?

Possible Answers:

Not enough information

$\small -\frac{2}{7}$

$\small -\frac{3}{4}$

$\small -\frac{7}{2}$

$\small \frac{7}{2}$

Correct answer:

$\small \frac{7}{2}$

Explanation:

By definition, lines are parallel if they have the same slope.

The problem states that line A has a slope of $\small \frac{7}{2}$ and that line X is parallel to it.

This means that line X must also have a slope of $\small \frac{7}{2}$ .

The y-intercept is not a determinant of lines being parallel or perpendicular.

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Example Question #3991 : Algebra 1

If a line is parallel to the line x+3y = 1 , what must be the slope of the other line?

Possible Answers:

$-\frac{1}{3}$

$\frac{1}{2}$

$\frac{1}{3}$

Correct answer:

$-\frac{1}{3}$

Explanation:

If a line is parallel to another line, they will never intersect. This means that their slopes will be the same.

The equation given is in standard form. Convert the equation to slope intercept form, y=mx+b , in order to determine the slope .

Subtract on both sides.

x+3y -x= 1-x

Simplify and reorganize the terms.

3y = -x+1

Divide by three on both sides.

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

Simplify both sides.

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

The slope of the parallel line must be $-\frac{1}{3}$ .

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Example Question #21 : How To Find The Slope Of Parallel Lines

What is the slope of a line that is parallel to y=2x+19 ?

Possible Answers:

$-\frac{1}{2}$

Correct answer:

Explanation:

To find the slope of a line parallel to any equation, the slopes will always be the same. We need to ensure we have y=mx+b form. stands for slope. In this case, m=2 which is also our answer.

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Example Question #22 : How To Find The Slope Of Parallel Lines

What is the slope of a line that is parallel to -7y-12x=13 ?

Possible Answers:

$\frac{12}{7}$

$-\frac{7}{12}$

$\frac{1}{7}$

Correct answer:

$\frac{12}{7}$

Explanation:

When finding the slope of a parallel line, we need to ensure we have y=mx+b form.

-7y-12x=13

We need to solve for .

By adding 12x both sides and dividing on both sides, we get $y=\frac{13+12x}{-7}$ stands for slope.

Our is $-\frac{12}{7}$ which is also the slope of the parallel line.

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Example Question #23 : How To Find The Slope Of Parallel Lines

What is the slope of a line that is parallel to 6x+8y=14?

Possible Answers:

$-\frac{1}{6}$

$\frac{3}{4}$

$\frac{4}{3}$

$-\frac{3}{4}$

Correct answer:

$-\frac{3}{4}$

Explanation:

When finding the slope of a parallel line, we need to ensure we have y=mx+b form.

6x+8y=14

We need to solve for .

By subtracting both sides and dividing on both sides, we get

$y=\frac{14-6x}{8}$

Recall that stands for slope.

Our is $-\frac{6}{8}$ or $-\frac{3}{4}$ which is also the slope of the parallel line.

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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 #3991 : Algebra 1

Example Question #3992 : Algebra 1

Example Question #3993 : Algebra 1

Example Question #3994 : Algebra 1

Example Question #3995 : Algebra 1

Example Question #3996 : Algebra 1

Example Question #3991 : Algebra 1

Example Question #21 : How To Find The Slope Of Parallel Lines

Example Question #22 : How To Find The Slope Of Parallel Lines

Example Question #23 : How To Find The Slope Of Parallel Lines

All Algebra 1 Resources

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