GMAT Math : Coordinate Geometry

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Example Questions

Example Question #3 : Calculating The Slope Of Parallel Lines

A given line is defined by the equation y=-5x+11 . What is the slope of any line parallel to this line?

Possible Answers:

$\frac{1}{5}$

$-\frac{1}{5}$

Correct answer:

Explanation:

Any line that is parallel to a line y=mx+b has a slope that is equal to the slope . Given y=-5x+11 , m=-5 and therefore any line parallel to the given line must have a slope of .

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Example Question #1 : Calculating The Slope Of Parallel Lines

A given line is defined by the equation $y=\frac{4}{3}x+12$ . What is the slope of any line parallel to this line?

Possible Answers:

$\frac{4}{3}$

$-\frac{4}{3}$

$\frac{3}{4}$

$-\frac{3}{4}$

Correct answer:

$\frac{4}{3}$

Explanation:

Any line that is parallel to a line y=mx+b has a slope that is equal to the slope . Given $y=\frac{4}{3}x+12$ , $m=\frac{4}{3}$ and therefore any line parallel to the given line must have a slope of $\frac{4}{3}$ .

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Example Question #1 : Calculating The Equation Of A Parallel Line

What is the equation of the line that is parallel to y=2x+10 and goes through point (5,1) ?

Possible Answers:

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

y=2x-9

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

y=-2x-9

Correct answer:

y=2x-9

Explanation:

Parallel lines have the same slope. Therefore, the slope of the new line is , as the equation of the original line is y=2x+10 (y=mx+b) ,with slope .

m=2 and (5,1) :

$y-y_{1}=m(x-x_{1})$

y-1=2(x-5)

y-1=2x-10

y=2x-10+1

y=2x-9

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Example Question #41 : Coordinate Geometry

Find the equation of a line that is parallel to 4x-2y=5 and passes through the point (4,1) .

Possible Answers:

$\dpi{100} \small y=-2x+7$

$\dpi{100} \small y=2x-7$

$\dpi{100} \small y< 2x-7$ None of the answers are correct.

$\dpi{100} \small y=2x+7$

$\dpi{100} \small y=-2x-7$

Correct answer:

$\dpi{100} \small y=2x-7$

Explanation:

The parallel line has the equation $\dpi{100} \small 4x-2y=5$ . We can find the slope by putting the equation into slope-intercept form, y = mx + b, where m is the slope and b is the intercept. $\dpi{100} \small 4x-2y=5$ becomes $\dpi{100} \small y=2x-\frac{5}{2}$ , so the slope is 2.

We know that our line must have an equation that looks like $\dpi{100} \small y=2x+b$ . Now we need the intercept. We can solve for b by plugging in the point (4, 1).

1 = 2(4) + b

b = –7

Then the line in question is $\dpi{100} \small y=2x-7$ .

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Example Question #3 : Calculating The Equation Of A Parallel Line

Given:

$\small f(x)=4x+13$

Which of the following is the equation of a line parallel to f(x) that has a y-intercept of ?

Possible Answers:

$\small \small \small f(x)=-\frac{1}{4}x-13$

$\small \small f(x)=-4x+13$

$\small \small \small f(x)=-\frac{1}{4}x+13$

$\small \small f(x)=\frac{1}{4}x+13$

$\small \small f(x)=4x-13$

Correct answer:

$\small \small f(x)=4x-13$

Explanation:

Parallel lines have the same slope, so our slope will still be 4. The y-intercept is just the "+b" at the end. In f(x) the y-intercept is 13. In this case, we need to have a y-intercept of -13, so our equation just becomes:

$\small \small f(x)=4x-13$

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Example Question #44 : Lines

Find the equation of the line that is parallel to the g(x) and passes through the point (8,9) .

$\small g(x)=6x+7$

Possible Answers:

$\small \small \small y=-\frac{1}{6}x-39$

$\small \small y=-6x-39$

$\small y=6x-39$

$\small \small y=\frac{1}{6}x-39$

$\small \small y=6x+39$

Correct answer:

$\small y=6x-39$

Explanation:

Two lines are parallel if they have the same slope. The slope of g(x) is 6, so eliminate anything without a slope of 6.

Recall slope intercept form which is y=mx+b .

We know that the line must have an m of 6 and an (x,y) of (8,9). Plug everything in and go from there.

$9=(6\cdot 8)+b$

$\small 9=48+b$

$\small b=9-48=-39$

So we get:

$\small y=6x-39$

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Example Question #3 : Calculating The Equation Of A Parallel Line

Given the function f(x)=7x-12 , which of the following is the equation of a line parallel to f(x) and has a -intercept of ?

Possible Answers:

g(x)=7x-8

$g(x)=-\frac{1}{7}x+8$

$g(x)=\frac{1}{7}x+8$

g(x)=-7x+2

g(x)=7x+8

Correct answer:

g(x)=7x+8

Explanation:

Given a line defined by the equation f(x)=mx+b with slope , any line that is parallel to also has a slope of . Since f(x)=7x-12 , the slope is and the slope of any line g(x) parallel to f(x) also has a slope of m=7 .

Since g(x) also needs to have a -intercept of , then the equation for g(x) must be g(x)=7x+8 .

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Example Question #16 : Parallel Lines

Given the function $f(x)=-\frac{6}{5}x+7$ , which of the following is the equation of a line parallel to f(x) and has a -intercept of ?

Possible Answers:

$g(x)=-\frac{6}{5}x-2$

$g(x)=\frac{5}{6}x-2$

$g(x)=-\frac{5}{6}x-2$

$g(x)=\frac{6}{5}x-2$

$g(x)=-\frac{6}{5}x+2$

Correct answer:

$g(x)=-\frac{6}{5}x-2$

Explanation:

Given a line defined by the equation f(x)=mx+b with slope , any line that is parallel to also has a slope of . Since $f(x)=-\frac{6}{5}x+7$ , the slope is $-\frac{6}{5}$ and the slope of any line g(x) parallel to f(x) also has a slope of $m=-\frac{6}{5}$ .

Since g(x) also needs to have a -intercept of , then the equation for g(x) must be $g(x)=-\frac{6}{5}x-2$ .

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Example Question #45 : Lines

Given the function f(x)=2x+5 , which of the following is the equation of a line parallel to f(x) and has a -intercept of ?

Possible Answers:

g(x)=-2x-17

g(x)=-2x+17

$g(x)=-\frac{1}{2}x-17$

g(x)=2x-17

g(x)=2x+17

Correct answer:

g(x)=2x-17

Explanation:

Given a line defined by the equation f(x)=mx+b with slope , any line that is parallel to also has a slope of . Since f(x)=2x+5 , the slope is and the slope of any line g(x) parallel to f(x) also has a slope of m=2 .

Since g(x) also needs to have a -intercept of , then the equation for g(x) must be g(x)=2x-17 .

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Example Question #42 : Coordinate Geometry

What is the equation of the line that is perpendicular to y=2x+10 and goes through point (5,1) ?

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

Perpendicular lines have slopes that are negative reciprocals of each other.

The slope for the given line is , from y=2x+10 (y=mx+b) , where is the slope. Therefore, the negative reciprocal is $-\frac{1}{2}$ .

$m=-\frac{1}{2}$ and (5,1) :

$y-y_{1}=m(x-x_{1})$

$y-1=-\frac{1}{2}(x-5)$

$y-1=-\frac{1}{2}x+\frac{5}{2}$

$y=-\frac{1}{2}x+\frac{5}{2}+1$

$y=-\frac{1}{2}x+\frac{5}{2}+\frac{2}{2}$

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

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GMAT Math : Coordinate Geometry

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #3 : Calculating The Slope Of Parallel Lines

Example Question #1 : Calculating The Slope Of Parallel Lines

Example Question #1 : Calculating The Equation Of A Parallel Line

Example Question #41 : Coordinate Geometry

Example Question #3 : Calculating The Equation Of A Parallel Line

Example Question #44 : Lines

Example Question #3 : Calculating The Equation Of A Parallel Line

Example Question #16 : Parallel Lines

Example Question #45 : Lines

Example Question #42 : Coordinate Geometry

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