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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 #141 : Parallel Lines

Determine if the lines are parallel and find their slopes:

y-6x=1

2y-12x=6

Possible Answers:

$No: slopes=\frac{1}{6},-4$

Yes: slope=6

No: slopes=2,-1

Yes: slope=3

Correct answer:

Yes: slope=6

Explanation:

In order to determine if two lines have the same slope first write them according to slope-intercept form, where "m" is the slope of the line:

y=mx+b

Do that for each line:

$y-6x=1\rightarrow y=6x+1$

$2y-12x=6\rightarrow 2y=12x+6\rightarrow y=6x+3$

Both lines have a slope of 6 which makes them parallel.

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Example Question #142 : Parallel Lines

Determine if the lines are parallel and find their slopes:

y=2x+3

2y=4x+3

Possible Answers:

$No: slopes:-2,\frac{1}{3}$

Yes: slope=-3

$Yes: slope=\frac{-1}{2}$

Yes: slope=2

Correct answer:

Yes: slope=2

Explanation:

In order to determine if two lines have the same slope first write them according to slope-intercept form, where "m" is the slope of the line:

y=mx+b

Do that for each line:

y=2x+3

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

Both lines have a slope of 2 which makes them parallel.

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Example Question #143 : Parallel Lines

Determine if the lines are parallel and find their slopes:

x-y=1

x-y=6

Possible Answers:

Yes: slope=1

Yes: slope=-2

Yes: slope=-1

No: slopes=-1,-3

Correct answer:

Yes: slope=1

Explanation:

In order to determine if two lines have the same slope first write them according to slope-intercept form, where "m" is the slope of the line:

y=mx+b

Do that for each line:

$x-y=1\rightarrow -y=-x+1\rightarrow y=x-1$

$x-y=6\rightarrow -y=-x+6\rightarrow y=x-6$

Both lines have a slope of 1 which makes them parallel.

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Example Question #91 : How To Find Out If Lines Are Parallel

Determine if the two lines are parallel and find their slopes:

6x+y=7

7x+2y=9

Possible Answers:

Yes: slope=-6

Yes: slope=-7

$No: slopes=-6,\frac{-7}{2}$

$Yes: slope=\frac{-7}{2}$

Correct answer:

$No: slopes=-6,\frac{-7}{2}$

Explanation:

In order to determine if two lines have the same slope first write them according to slope-intercept form, where "m" is the slope of the line:

y=mx+b

Do that for each line:

$6x+y=7\rightarrow y=-6x+7$

$7x+2y=9\rightarrow 2y=-7x+9\rightarrow y=\frac{-7}{2}x+\frac{9}{2}$

The first line has a slope of -6, while the second has a slope of -7/2 meaning the lines are not parallel.

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Example Question #92 : How To Find Out If Lines Are Parallel

Determine if the lines are parallel and find their slopes:

x+2y=4

x-2y=4

Possible Answers:

$Yes: slope=\frac{1}{2}$

Yes: slope=-2

$Yes: slope=\frac{-1}{2}$

$No: slopes= \frac{-1}{2},\frac{1}{2}$

Correct answer:

$No: slopes= \frac{-1}{2},\frac{1}{2}$

Explanation:

In order to determine if two lines have the same slope first write them according to slope-intercept form, where "m" is the slope of the line:

y=mx+b

Do that for each line:

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

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

The first line has a slope of -1/2, while the second has a slope of 1/2 meaning the lines are not parallel.

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Example Question #93 : How To Find Out If Lines Are Parallel

Determine if the lines are parallel and find their slopes:

4y-2=x

6y-3=2x

Possible Answers:

$No: slopes:\frac{1}{4},\frac{1}{3}$

$Yes: slope=\frac{1}{3}$

Yes: slope=-1

$Yes: slope=\frac{1}{2}$

Correct answer:

$No: slopes:\frac{1}{4},\frac{1}{3}$

Explanation:

In order to determine if two lines have the same slope first write them according to slope-intercept form, where "m" is the slope of the line:

y=mx+b

Do that for each line:

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

$6y-3=2x\rightarrow 6y=2x+3\rightarrow y=\frac{1}{3}x+\frac{1}{2}$

The first line has a slope of 1/4, while the second has a slope of 1/3 meaning the lines are not parallel.

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Example Question #94 : How To Find Out If Lines Are Parallel

Determine if the lines are parallel and find their slopes:

x-y=4

2x-3y=4

Possible Answers:

Yes: slope=-1

$No: slopes=1,\frac{2}{3}$

$Yes: slope=\frac{3}{2}$

$Yes: slope=\frac{2}{3}$

Correct answer:

$No: slopes=1,\frac{2}{3}$

Explanation:

In order to determine if two lines have the same slope first write them according to slope-intercept form, where "m" is the slope of the line:

y=mx+b

Do that for each line:

$x-y=4\rightarrow -y=-x+4\rightarrow y=x-4$

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

The first line has a slope of 1, while the second has a slope of 2/3 meaning the lines are not parallel.

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Example Question #148 : Parallel Lines

Determine if the lines are parallel and find their slopes:

6x+y=12

5x+2y=15

Possible Answers:

$No: slopes=-6,\frac{-5}{2}$

Yes: slope=-2

No: slopes=1,-4

Yes: slope=-6

Correct answer:

$No: slopes=-6,\frac{-5}{2}$

Explanation:

In order to determine if two lines have the same slope first write them according to slope-intercept form, where "m" is the slope of the line:

y=mx+b

Do that for each line:

$6x+y=12\rightarrow y=-6x+12$

$5x+2y=15\rightarrow 2y=-5x+15\rightarrow y=\frac{-5}{2}x+3$

The first line has a slope of -6, while the second has a slope of -5/2 meaning the lines are not parallel.

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Example Question #4101 : Algebra 1

Determine if the lines are parallel and find their slopes:

y-3x=12

y+2x=6

Possible Answers:

$Yes: slope=\frac{1}{3}$

No: slopes=3,-2

Yes: slope=-1

$No: slopes=-1,\frac{2}{3}$

Correct answer:

No: slopes=3,-2

Explanation:

In order to determine if two lines have the same slope first write them according to slope-intercept form, where "m" is the slope of the line:

y=mx+b

Do that for each line:

$y-3x=12\rightarrow y=3x+12$

$y+2x=6\rightarrow y=-2x+6$

The first line has a slope of 3, while the second has a slope of -2 meaning the lines are not parallel.

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Example Question #571 : Equations Of Lines

Find the line that is parallel to the following:

6y = -42x + 36

Possible Answers:

6y = -36x + 6

-9x = -63x + 9

-8y = 56x + 64

y = -42x - 26

7y = -42x -14

Correct answer:

-8y = 56x + 64

Explanation:

Two lines are parallel when they have the same slope. We can compare slopes when we write the equation of the line in slope-intercept form

y = mx+b

where m is the slope. Given the original equation

6y = -42x + 36

we must write it in slope-intercept form to find the slope. To do this, we will divide each term by 6. We get

$\frac{6y}{6} = \frac{-42x}{6} + \frac{36}{6}$

y = -7x + 6

Therefore, the slope of the original line is -7. A line that is parallel to this line needs to have a slope of -7.

Let's look at the equation of the line

-8y = 56x + 64

We must write it in slope-intercept form. To do this, we will divide each term by -8. We get

$\frac{-8y}{-8} = \frac{56x}{-8} + \frac{64}{-8}$

y = -7x - 8

The slope of this line is -7. Therefore, it is parallel to the original line.

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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 #141 : Parallel Lines

Example Question #142 : Parallel Lines

Example Question #143 : Parallel Lines

Example Question #91 : How To Find Out If Lines Are Parallel

Example Question #92 : How To Find Out If Lines Are Parallel

Example Question #93 : How To Find Out If Lines Are Parallel

Example Question #94 : How To Find Out If Lines Are Parallel

Example Question #148 : Parallel Lines

Example Question #4101 : Algebra 1

Example Question #571 : Equations Of Lines

All Algebra 1 Resources

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