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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 #68 : How To Find Out If Lines Are Parallel

Find a line parallel to the line with the equation:

3x-2y=12

Possible Answers:

y=3x+3

y=2x-9

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

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

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.

3x-2y=12

We need to isolate on the left side of the equation. Subtract from both sides of the equation.

3x-3x-2y=12-3x

Simplify.

-2y=12-3x

Divide both sides of the equation by .

$\frac{-2y}{-2}=\frac{12}{-2}- \left ( \frac{3x}{-2}\right )$

Simplify. Remember that when a positive number is divided by a negative number, the answer is always negative.

$y=-6- \left ( -\frac{3}{2}x\right )$

Subtracting a negative number is the same as adding a positive number. Rewrite.

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

Rearrange terms to match the slope-intercept form.

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

In the given equation:

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

Parallel lines share the same slope.

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

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

Report an Error

Example Question #69 : How To Find Out If Lines Are Parallel

Find a line parallel to the line with the equation:

10x+6y=70

Possible Answers:

y=5x+3

$y=-\frac{5}{3}x-9$

$y=-\frac{2}{5}x+8$

y=-2x+6

Correct answer:

$y=-\frac{5}{3}x-9$

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.

10x+6y=70

We need to isolate on the left side of the equation. Subtract 10x from both sides of the equation.

10x-10x+6y=70-10x

Simplify.

6y=70-10x

Divide both sides of the eqaution by .

$\frac{6y}{6}=\frac{70}{6}-\frac{10x}{6}$

Simplify.

$y=\frac{35}{3}-\frac{5}{3}x$

Rearrange terms to match the slope-intercept form.

$y=-\frac{5}{3}x+\frac{35}{3}$

In the given equation:

$m=-\frac{5}{3}$

Parallel lines share the same slope.

Only one of the choices has a slope of $-\frac{5}{3}$ .

$y=-\frac{5}{3}x-9$

Report an Error

Example Question #70 : How To Find Out If Lines Are Parallel

Find a line parallel to the line with the equation:

6x-y=12

Possible Answers:

y=-6x-7

$y=\frac{1}{6}x+3$

y=6x-7

y=-x+5

Correct answer:

y=6x-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.

6x-y=12

We need to isolate on the left side of the equation. Subtract from both sides of the equation.

6x-6x-y=12-6x

Simplify.

-y=12-6x

Divide both sides of the equation by . Rember that when a positive number is divided by a negative number, the answer is always negative. Also, when a negative number is divided by a negative number, the answer is always positive.

$\frac{-y}{-1}=\frac{12}{-1}-\frac{6x}{-1}$

Simplify.

y=-12-(-6x)

Subtracting a negative number is the same as adding a positive number. Rewrite.

y=-12+6x

Rearrange terms to match the slope-intercept form.

y=6x-12

In the given equation:

m=6

Parallel lines share the same slope.

Only one of the choices has a slope of .

y=6x-7

Report an Error

Example Question #113 : Parallel Lines

Find a line parallel to the line with the equation:

4x-10y=11

Possible Answers:

$y=\frac{2}{5}x+6$

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

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

y=-10x-2

Correct answer:

$y=\frac{2}{5}x+6$

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.

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

4x-10y=11

We need to isolate on the left side of the equation. Subtract from both sides of the equation.

4x-4x-10y=11-4x

Simplify.

-10y=11-4x

Divide both sides of the equation by .

$\frac{-10y}{-10}=\frac{11}{-10}-\left ( \frac{4x}{-10} \right )$

Simplify. Remember that when a positive number is divided by a negative number, the answer is always negative.

$y=-\frac{11}{10}-\left ( -\frac{4}{10} x\right )$

Subtracting a negative number is the same as adding a positive number. Rewrite.

$y=-\frac{11}{10}+\frac{4}{10} x$

Reduce.

$y=-\frac{11}{10}+\frac{2}{5} x$

Rearrange terms to match the slope-intercept form.

$y=\frac{2}{5}x-\frac{11}{10}$

In the given equation:

$m=\frac{2}{5}$

Parallel lines share the same slope.

Only one of the choices has a slope of $\frac{2}{5}$ .

$y=\frac{2}{5}x+6$

Report an Error

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

Find a line parallel to the line with the equation:

12x+6y=18

Possible Answers:

$y=\frac{1}{2}x-8$

y=2x-6

y=-x+6

y=-2x+6

Correct answer:

y=-2x+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.

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

12x+6y=18

We need to isolate on the left side of the equation. Subtract 12x from both sides of the equation.

12x-12x+6y=18-12x

Simplify.

6y=18-12x

Divide both sides of the equation by .

$\frac{6y}{6}=\frac{18}6{}-\frac{12x}{6}$

Simplify.

y=3-2x

Rearrange terms to match the slope-intercept form.

y=-2x+3

In the given equation:

m=-2

Parallel lines share the same slope.

Only one of the choices has a slope of .

y=-2x+6

Report an Error

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

Find a line parallel to the line with the equation:

5x+5y=10

Possible Answers:

y=x+3

$y=\frac{1}{5}x-9$

y=-x-2

y=5x+6

Correct answer:

y=-x-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.

5x+5y=10

We need to isolate on the left side of the equation. Subtract from both sides of the equation.

5x-5x+5y=10-5x

Simplify.

5y=10-5x

Divide both sides of the equation by .

$\frac{5y}{5}=\frac{10}{5}-\frac{5x}{5}$

Simplify.

y=2-x

Rearrange terms to match the slope-intercept form.

y=-x+2

In the given equation:

m=-1

Parallel lines share the same slope.

Only one of the choices has a slope of .

y=-x-2

Report an Error

Example Question #121 : Parallel Lines

Which of the following pairs of lines are parallel?

Possible Answers:

y=4x-2

y=3x+9

$y=\frac{1}{2}x-8$

y=2x-1

y=2x-5

y=-2x+2

y=2x-2

y=2x+12

Correct answer:

y=2x-2

y=2x+12

Explanation:

Lines can be written in the slope-intercept form:

y=mx+b

In this form, equals the slope and represents where the line intersects the y-axis.

Parallel lines have the same slope: .

Only one choice contains tow lines with the same slope.

y=2x-2

y=2x+12

The slope for both lines in this pair is m=2 .

Report an Error

Example Question #73 : How To Find Out If Lines Are Parallel

Find a line parallel to the line with the equation:

7y-6x=1

Possible Answers:

y=-6x+12

$y=\frac{6}{7}x+\frac{1}{2}$

$y=\frac{7}{6}x+\frac{1}{3}$

$y=-\frac{6}{7}x-7$

Correct answer:

$y=\frac{6}{7}x+\frac{1}{2}$

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.

7y-6x=1

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

7y-6x+6x=1+6x

Simplify.

7y=1+6x

Divide both sides of the equation by .

$\frac{7y}{7}=\frac{1}{7}+\frac{6x}{7}$

Simplify.

$y=\frac{1}{7}+\frac{6}{7}x$

Rearrange terms to match the slope-intercept form.

$y=\frac{6}{7}x+\frac{1}{7}$

In the given equation:

$m=\frac{6}{7}$

Parallel lines share the same slope.

Only one of the choices has a slope of $\frac{6}{7}$ .

$y=\frac{6}{7}x+\frac{1}{2}$

Report an Error

Example Question #74 : How To Find Out If Lines Are Parallel

Find a line parallel to the line with the equation:

9x-5y=16

Possible Answers:

$y=-\frac{9}{5}x-1$

$y=\frac{9}{5}x+5$

$y=\frac{5}{9}x-\frac{12}{13}$

y=9x+2

Correct answer:

$y=\frac{9}{5}x+5$

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.

9x-5y=16

We need to isolate on the left side of the equation. Subtract from both sides of the equation.

9x-9x-5y=16-9x

Simplify.

-5y=16-9x

Divide both sides of the equation by .

$\frac{-5y}{-5}=\frac{16}{-5}-\left ( \frac{9x}{-5} \right )$

Simplify. Remember that when a positive number is divided by a negative number, the answer is always negative.

. $y=-\frac{16}{5}-\left ( -\frac{9}{5}x\right )$

Subtracting a negative number is the same as adding a positive number. Rewrite.

$y=-\frac{16}{5}+\frac{9}{5}x$

Rearrange terms to match the slope-intercept form.

$y=\frac{9}{5}x-\frac{16}{5}$

In the given equation:

$m=\frac{9}{5}$

Parallel lines share the same slope.

Only one of the choices has a slope of $\frac{9}{5}$ .

$y=\frac{9}{5}x+5$

Report an Error

Example Question #122 : Parallel Lines

Find a line parallel to the line with the equation:

2x-y=1

Possible Answers:

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

$y=-2x-\frac{1}{7}$

$y=-x-\pi$

$y=2x+\pi$

Correct answer:

$y=2x+\pi$

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.

2x-y=1

We need to isolate on the left side of the equation. Subtract from both sides of the equation.

2x-2x-y=1-2x

Simplify.

-y=1-2x

Divide both sides of the equation by .

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

Simplify. Remember that when a positive number is divided by a negative number, the answer is always negative.

$y=-1-\left ( -2x\right )$

Subtracting a negative number is the same as adding a positive number. Rewrite.

y=-1+2x

Rearrange terms to match the slope-intercept form.

y=2x-1

n the given equation:

m=2

Parallel lines share the same slope.

Only one of the choices has a slope of .

$y=2x+\pi$

Report an Error

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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 #68 : How To Find Out If Lines Are Parallel

Example Question #69 : How To Find Out If Lines Are Parallel

Example Question #70 : How To Find Out If Lines Are Parallel

Example Question #113 : Parallel Lines

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

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

Example Question #121 : Parallel Lines

Example Question #73 : How To Find Out If Lines Are Parallel

Example Question #74 : How To Find Out If Lines Are Parallel

Example Question #122 : Parallel Lines

All Algebra 1 Resources

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