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SSAT Upper Level Math : How to find the equation of a parallel line

Study concepts, example questions & explanations for SSAT Upper Level Math

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All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #172 : Lines

Find the equation of the line that goes through the point (-3, 1) and is parallel to the line with the equation y=2x-1 .

Possible Answers:

y=2x+7

y=-2x+7

y=2x-3

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

Correct answer:

y=2x+7

Explanation:

Because the two lines are parallel, we know that the slope of the line we need to find must also be .

We can then plug in the given point and the slope into the equation of a line to find the y-intercept.

1=2(-3)+b

-6+b=1

b=7

Now, we can write the equation of the line.

y=2x+7

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Example Question #173 : Lines

Find the equation of the line that passes through the point (1, -2) and is parallel to the line with the equation $y=\frac{3}{2}x-1$ .

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

Because the two lines are parallel, we know that the slope of the line we need to find must also be $\frac{3}{2}$ .

Now, we can plug in the point given by the question to find the y-intercept.

$-2=\frac{3}{2}(1)+b$

$b+\frac{3}{2}=-2$

$b=-\frac{7}{2}$

From this, we can write the following equation:

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

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Example Question #174 : Lines

Find the equation of the line that passes through the point (-2, -4) and is parallel to the line with the equation y=3x-2 .

Possible Answers:

y=3x+2

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

y=-3x+2

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

Correct answer:

y=3x+2

Explanation:

Because the two lines are parallel, we know that the slope of the line we need to find must also be .

Next, plug in the point given by the question to find the y-intercept of the line.

-4=3(-2)+b

b-6=-4

b=2

Now, we know that the equation of the line must be y=3x+2 .

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Example Question #175 : Lines

Find the equation of the line that passes through the point (1, 2) and is parallel to the line with the equation y=-2x-1 .

Possible Answers:

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

y=2x-3

y=-2x-4

y=-2x+4

Correct answer:

y=-2x+4

Explanation:

Because the two lines are parallel, we know that the slope of the line we need to find must also be .

Next, plug in the point given by the question to find the y-intercept of the line.

2=-2(1)+b

b-2=2

b=4

Now, we know the equation of the line must be y=-2x+4 .

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Example Question #231 : Geometry

Find the equation of the line that passes through the point (-2, 5) and is parallel to the line with the equation y=-x-2 .

Possible Answers:

y=x+3

y=-x+6

y=-x+3

y=x-4

Correct answer:

y=-x+3

Explanation:

Because the two lines are parallel, we know that the slope of the line we need to find must also be .

Next, plug in the point given by the question to find the y-intercept of the line.

5=-1(-2)+b

b+2=5

b=3

Now, we can write the equation for the line: y=-x+3

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Example Question #232 : Geometry

Find the equation of the line that passes through the point (-2, 3) and is parallel to the line with the equation $y=\frac{1}{2}x-2$ .

Possible Answers:

y=2x-1

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

y=-2x+4

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

Correct answer:

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

Explanation:

Because the two lines are parallel, we know that the slope of the line we need to find must also be $\frac{1}{2}$ .

Next, plug in the point given by the question to find the y-intercept of the line.

$3=\frac{1}{2}(-2)+b$

b-1=3

b=4

Now, we knwo the equation of the line must be $y=\frac{1}{2}x+4$ .

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Example Question #233 : Geometry

Find the equation of the line that passes through the point (2, 8) and is parallel to the line with the equation y=4x-1 .

Possible Answers:

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

y=4x

y=4x-2

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

Correct answer:

y=4x

Explanation:

Because the two lines are parallel, we know that the slope of the line we need to find must also be .

Next, plug in the point given by the question to find the y-intercept of the line.

8=4(2)+b

b+8=8

b=0

Thus, the equation of the line must be y=8x .

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Example Question #234 : Geometry

Find the equation of the line that passes through the point (10, 2) and is parallel to the line with the equation $y=\frac{1}{5}x-2$ .

Possible Answers:

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

y=-5x+2

$y=\frac{1}{5}x-6$

y=5x-1

Correct answer:

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

Explanation:

Because the two lines are parallel, we know that the slope of the line we need to find must also be $\frac{1}{5}$ .

Next, plug in the point given by the question to find the y-intercept of the line.

$2=\frac{1}{5}(10)+b$

b+2=2

b=0

The equation of the line is $y=\frac{1}{5}x$ .

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Example Question #235 : Geometry

Find the equation of the line that passes through the point (3, 1) and is parallel to the line with the equation $y=\frac{1}{3}x-9$ .

Possible Answers:

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

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

y=-3x

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

Correct answer:

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

Explanation:

Because the two lines are parallel, we know that the slope of the line we need to find must also be $\frac{1}{3}$ .

Next, plug in the point given by the question to find the y-intercept of the line.

$1=\frac{1}{3}(3)+b$

b+1=1

b=0

The equation of the line is $y=\frac{1}{3}x$ .

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Example Question #236 : Geometry

Find the equation of the line that passes through the point $\left(\frac{1}{2}, 4\right)$ and is parallel to the line with the equation y=2x-1 .

Possible Answers:

y=2x+3

y=2x-2

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

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

Correct answer:

y=2x+3

Explanation:

Because the two lines are parallel, we know that the slope of the line we need to find must also be .

Next, plug in the point given by the question to find the y-intercept of the line.

$4=\frac{1}{2}(2)+b$

b+1=4

b=3

Now, we know the equation of the line must be y=2x+3 .

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : How to find the equation of a parallel line

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #172 : Lines

Example Question #173 : Lines

Example Question #174 : Lines

Example Question #175 : Lines

Example Question #231 : Geometry

Example Question #232 : Geometry

Example Question #233 : Geometry

Example Question #234 : Geometry

Example Question #235 : Geometry

Example Question #236 : Geometry

All SSAT Upper Level Math Resources

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