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SSAT Upper Level Math : Parallel Lines

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Example Questions

Example Question #1 : How To Find The Equation Of A Parallel Line

If the line through the points (5, –3) and (–2, p) is parallel to the line y = –2x – 3, what is the value of p ?

Possible Answers:

–10

–17

Correct answer:

Explanation:

Since the lines are parallel, the slopes must be the same. Therefore, (p+3) divided by (–2–5) must equal –2. 11 is the only choice that makes that equation true. This can be solved by setting up the equation and solving for p, or by plugging in the other answer choices for p.

$\frac{p--3}{-2-5}=\frac{p+3}{-2-5}=-2$

$\frac{p+3}{-7}=-2$

$(\frac{p+3}{-7})-7=-2(-7)$

p+3=14

p=11

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Example Question #171 : Coordinate Geometry

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:

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

y=2x-3

y=-2x+7

y=2x+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 #172 : Coordinate Geometry

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:

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

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

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

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

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 #221 : Geometry

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 #171 : 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=-2x+4

y=2x-3

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

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 #174 : Coordinate 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-4

y=-x+3

y=-x+6

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 #175 : Coordinate 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=-2x+4

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

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

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 #176 : Coordinate 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:

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

y=4x

y=4x-2

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

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 #177 : Coordinate 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-1

y=-5x+2

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

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 #11 : How To Find The Equation Of A Parallel Line

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:

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

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

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

y=-3x

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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SSAT Upper Level Math : Parallel Lines

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #1 : How To Find The Equation Of A Parallel Line

Example Question #171 : Coordinate Geometry

Example Question #172 : Coordinate Geometry

Example Question #221 : Geometry

Example Question #171 : Lines

Example Question #174 : Coordinate Geometry

Example Question #175 : Coordinate Geometry

Example Question #176 : Coordinate Geometry

Example Question #177 : Coordinate Geometry

Example Question #11 : How To Find The Equation Of A Parallel Line

All SSAT Upper Level Math Resources

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