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GED Math : Coordinate Geometry

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Example Questions

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Example Question #21 : Slope

What is the slope of the line that passes through the points (-5, 1) and (-2, 5) ?

Possible Answers:

$\frac{4}{3}$

$\frac{3}{4}$

$-\frac{3}{4}$

Correct answer:

$\frac{4}{3}$

Explanation:

Recall the how to find the slope of a line:

$\frac{y_2-y_1}{x_2-x_1}$

Plug in the given points.

$\text{Slope}=\frac{5-1}{-2-(-5)}$

Simplify to find the slope.

$\text{Slope}=\frac{5-1}{-2-(-5)}=\frac{4}{3}$

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Example Question #21 : Slope

What is the slope of the line that goes through the points (10, 4) and (-5, 6) ?

Possible Answers:

$\frac{2}{15}$

$-\frac{15}{2}$

$\frac{15}{2}$

$-\frac{2}{15}$

Correct answer:

$-\frac{2}{15}$

Explanation:

Recall how to find the slope of a line:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Plug in the given points to find the slope.

$\text{Slope}=\frac{6-4}{-5-10}=-\frac{2}{15}$

The line has a slope of $-\frac{2}{15}$ .

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Example Question #23 : Slope

Find the slope of the line connecting the following points.

(19,47) (99,123)

Possible Answers:

$\frac{9}{20}$

$\frac{19}{80}$

$\frac{77}{80}$

$\frac{19}{20}$

Correct answer:

$\frac{19}{20}$

Explanation:

Find the slope of the line connecting the following points.

(19,47) (99,123)

To find slope, use the following formula.

$m=\frac{y_1-y_2}{x_1-x_2}$

Remember, slope is rise over run.

Now, let's plug and chug to get our answer.

$m=\frac{123-47}{99-19}=\frac{76}{80}$

Now, simplify our answer to get our final answer.

$\frac{76}{80}=\frac{38}{40}=\frac{19}{20}$

So our answer is

$\frac{19}{20}$

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Example Question #31 : Coordinate Geometry

What is the slope of the graph?

Linear1 page 001

Possible Answers:

$\frac{3}{2}$

$\frac{2}{3}$

Correct answer:

$\frac{3}{2}$

Explanation:

Slope is $\frac{rise}{run}$ .

We can pick any two points on the graph and count the rise and run. This graph goes through (0,0), so lets pick that point. It also looks like (2,3) is on the graph.

So, from (0,0) to (2,3), you go up 3, and over 2.

This makes our slope $\frac{3}{2}$

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Example Question #25 : Slope

Find the slope of the line connecting the points and .

Possible Answers:

$\frac{12}{101}$

$\frac{12}{17}$

$\frac{2}{17}$

$\frac{101}{12}$

Correct answer:

$\frac{12}{101}$

Explanation:

Find the slope of the line connecting the points and .

To find our slope, we need to recall "Rise over Run." This can also be thought of as change in y over change in x.

$\frac{\delta y}{\delta x}=\frac{y_2-y_1}{x_2-x_1}$

Now, all we need to do is plug in our points and solve. It doesn't matter which pairs are x and which are y, but we must keep it consistent.

$\frac{\delta y}{\delta x}=\frac{65-17}{413-9}=\frac{48}{404}$

Now let's simplify:

$\frac{48}{404}=\frac{12}{101}$

So, we get $\frac{12}{101}$ which cannot be reduced, so we are all set!

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Example Question #31 : Coordinate Geometry

What is the slope of the line perpendicular to the line running between the points (201,31) and (834,3) ?

Possible Answers:

$\frac{34}{1035}$

$\frac{633}{28}$

$\frac{-28}{633}$

$\frac{28}{633}$

$\frac{-633}{28}$

Correct answer:

$\frac{633}{28}$

Explanation:

Recall that slope is calculated as:

$\frac{rise}{run}$

This could be represented, using your two points, as:

$\frac{y_2-y_1}{x_2-x_1}$

Based on your data, this would be:

$\frac{3-31}{834-201}=\frac{-28}{633}$

Remember, the question asks for the slope that is perpendicular to this slope! Don't forget this point! The perpendicular slope is opposite and reciprocal.

Therefore, it is:

$\frac{633}{28}$

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Example Question #1 : X Intercept And Y Intercept

Which of the following equations has as its graph a line with -intercept 9?

Possible Answers:

x = 9 y + 81

9x = y + 81

x+ 9 y = 81

9x+ y = 81

Correct answer:

x+ 9 y = 81

Explanation:

The equation in which y = 9 when x=0 is graphed by a line that includes point (0,9) - that is, its -intercept is 9. Therefore, substitute 0 for in each equation and solve for .

x = 9 y + 81

0 = 9 y + 81

9y = -81

y = -9

9x = y + 81

$9 \cdot 0 = y + 81$

0 = y + 81

y = -81

9x+ y = 81

$9 \cdot 0 + y = 81$

0 + y = 81

y = 81

x+ 9 y = 81

0+ 9 y = 81

9 y = 81

y = 9

The correct choice is x+ 9 y = 81 , since (0,9) is a solution of this equation.

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Example Question #1 : X Intercept And Y Intercept

Which of the following equations has as its graph a line with -intercept ?

Possible Answers:

x + 9y = 81

y = 9x + 81

9y = x + 81

9x+ y = 81

Correct answer:

y = 9x + 81

Explanation:

The equation in which x = - 9 when y=0 is graphed by a line that includes point (-9,0) - that is, its -intercept is . Therefore, substitute 0 for in each equation and solve for .

9y = x + 81

$9 \cdot 0 = x + 81$

0 = x + 81

x = -81

9x+ y = 81

9x+ 0 = 81

9x = 81

x = 9

x + 9y = 81

$x + 9 \cdot 0 = 81$

x + 0 = 81

x = 81

y = 9x + 81

0= 9x + 81

-81 = 9x

x = -9

The correct choice is y = 9x + 81 , since (-9,0) is a solution of this equation.

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Example Question #1 : X Intercept And Y Intercept

Find the and -intercepts of the following equation:

y = 3x + 6

Possible Answers:

x-intercept: -2

y-intercept: -6

x-intercept: 2

y-intercept: -6

x-intercept: -6

y-intercept: 2

x-intercept: -2

y-intercept: 6

x-intercept: 6

y-intercept: -2

Correct answer:

x-intercept: -2

y-intercept: 6

Explanation:

To find the x-intercept , we need to set equal to 0 in our equation:

0 = 3x + 6

Now solve for :

-6 = 3x

-2 = x

To find the y-intercept , we need to set equal to 0 in our equation:

y = 3(0) + 6

Now solve for :

y = 0 + 6

y = 6

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Example Question #1 : X Intercept And Y Intercept

Find the and -intercepts for the following equation:

4x - 6y = 12

Possible Answers:

x-intercept: -3

y-intercept: 2

x-intercept: -2

y-intercept: -3

x-intercept: -2

y-intercept: 3

x-intercept: 3

y-intercept: -2

x-intercept: 3

y-intercept: 2

Correct answer:

x-intercept: 3

y-intercept: -2

Explanation:

To find the x-intercept , set the equal to 0:

4x - 6(0) = 12

Then solve for :

4x = 12

x = 3

To find the y-intercept , set the equal to 0:

4(0) - 6y = 12

Then solve for :

-6y = 12

y = -2

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GED Math : Coordinate Geometry

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #21 : Slope

Example Question #21 : Slope

Example Question #23 : Slope

Example Question #31 : Coordinate Geometry

Example Question #25 : Slope

Example Question #31 : Coordinate Geometry

Example Question #1 : X Intercept And Y Intercept

Example Question #1 : X Intercept And Y Intercept

Example Question #1 : X Intercept And Y Intercept

Example Question #1 : X Intercept And Y Intercept

All GED Math Resources

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