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Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

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10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #63 : How To Find Out If Lines Are Parallel

Find a line parallel to the line with the equation:

$y=-\frac{2}{13}x-9$

Possible Answers:

$y=\frac{2}{13}$

y=-2x-8

$y=\frac{2}{13}x+3$

$y=-\frac{2}{13}x+88$

Correct answer:

$y=-\frac{2}{13}x+88$

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:

$m=-\frac{2}{13}$

Parallel lines share the same slope.

Only one of the choices has a slope of $-\frac{2}{13}$ .

$y=-\frac{2}{13}x+88$

Report an Error

Example Question #64 : How To Find Out If Lines Are Parallel

Find a line parallel to the line with the equation:

y=50x-4

Possible Answers:

$y=\frac{1}{50}x+36$

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

y=-50x+63

y=50x+50

Correct answer:

y=50x+50

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=50

Parallel lines share the same slope.

Only one of the choices has a slope of .

y=50x+50

Report an Error

Example Question #65 : How To Find Out If Lines Are Parallel

Find a line parallel to the line with the equation:

2y-4x=16

Possible Answers:

y=4x+3

y=2x+6

y=-2x+9

$y=\frac{1}{2}x-9$

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.

2y-4x=16

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

2y-4x+4x=16+4x

Simplify.

2y=16+4x

Divide both sides of the equation by .

$\frac{2y}{2}=\frac{16}{2}+\frac{4x}{2}$

Simplify.

y=8+2x

Rearrange terms to match the slope-intercept form.

y=2x+8

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 #4061 : Algebra 1

Find a line parallel to the line with the equation:

16y-8x=11

Possible Answers:

y=8x+6

$y=\frac{1}{2}x+9$

y=-16x+2

y=2x-8

Correct answer:

$y=\frac{1}{2}x+9$

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.

16y-8x=11

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

16y-8x+8x=11+8x

Simplify.

16y=11+8x

Divide both sides of the equation by .

$\frac{16y}{16}=\frac{11}{16}+\frac{8x}{16}$

Simplify.

$y=\frac{11}{16}+\frac{1}{2}x$

Rearrange terms to match the slope-intercept form.

$y=\frac{1}{2}x+\frac{11}{16}$

In the given equation:

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

Parallel lines share the same slope.

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

$y=\frac{1}{2}x+9$

Report an Error

Example Question #64 : How To Find Out If Lines Are Parallel

Find a line parallel to the line with the equation:

4x-5y=10

Possible Answers:

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

$y=\frac{5}{4}x+6$

y=-5x+6

y=4x+10

Correct answer:

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

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.

4x-5y=10

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

4x-4x-5y=10-4x

Simplify.

-5y=10-4x

Divide both sides of the equation by .

$\frac{-5y}{-5}=\frac{10}{-5}-\frac{4x}{-5}$

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

$y=(-2)-\left ( -\frac{4}{5}x\right )$

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

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

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 $\frac{4}{5}$ .

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

Report an Error

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

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Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #63 : How To Find Out If Lines Are Parallel

Example Question #64 : How To Find Out If Lines Are Parallel

Example Question #65 : How To Find Out If Lines Are Parallel

Example Question #4061 : Algebra 1

Example Question #64 : How To Find Out If Lines Are Parallel

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

All Algebra 1 Resources

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