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

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Example Questions

Example Question #181 : Coordinate Geometry

Find the equation of the line that passes through the point $\left(2, \frac{1}{4}\right)$ and is parallel to the line with the equation $y=\frac{1}{8}x-2$ .

Possible Answers:

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

y=-8x

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

$y=\frac{1}{8}x+3$

Correct answer:

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

Explanation:

Because the two lines are parallel, we know that the slope of the line we need to find must also be $\frac{1}{8}$ .

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

$\frac{1}{4}=\frac{1}{8}(2)+b$

$b+\frac{1}{4}=\frac{1}{4}$

b=0 .

We can then write the equation of the line: $y=\frac{1}{8}x$

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Example Question #5 : How To Find The Equation Of A Parallel Line

Which of these formulas could be a formula for a line perpendicular to the line 2x + 3y = 16 ?

Possible Answers:

6y - 9x = 16.5

4x + 6y = 24

6y + 9x = 16

3y - 4x = 23

4y - 9x = 24

Correct answer:

6y - 9x = 16.5

Explanation:

This is a two-step problem. First, the slope of the original line needs to be found. The slope will be represented by "" when the line is in -intercept form (y=mx+b) .

2x +3y = 16

3y = -2x +16

$y = \left(\frac{-2}{3}\right)x +\left(\frac{16}{3}\right)$

So the slope of the original line is $-\frac{2}{3}$ . A line with perpendicular slope will have a slope that is the inverse reciprocal of the original. So in this case, the slope would be $\frac{3}{2}$ . The second step is finding which line will give you that slope. For the correct answer, we find the following:

6y - 9x = 16.5

6y = 9x +16.5

$y= \left(\frac{3}{2}x\right) +\left(\frac{16.5}{6}\right)$

So, the slope is $\frac{3}{2}$ , and this line is perpendicular to the original.

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Example Question #21 : How To Find The Equation Of A Parallel Line

Find the equation of a line that goes through the point (0, 4) and is parallel to the line with the equation y=4x-2 .

Possible Answers:

y=4x-4

y=-4x+4

y=4x+4

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

Correct answer:

y=4x+4

Explanation:

For lines to be parallel, they must have the same slope. The slope of the line we are looking for then must be .

The point that's given in the equation is also the y-intercept.

Using these two pieces of information, we know that the equation for the line must be y=4x+4

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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 #181 : Coordinate Geometry

Example Question #5 : How To Find The Equation Of A Parallel Line

Example Question #21 : How To Find The Equation Of A Parallel Line

All SSAT Upper Level Math Resources

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