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GED Math : Geometry and Graphs

Study concepts, example questions & explanations for GED Math

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4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : Coordinate Geometry

In which quadrant is the point (4, -7 ) located in the coordinate plane?

Possible Answers:

Quadrant II

Quadrant IV

Quadrant I

Quadrant III

Correct answer:

Quadrant IV

Explanation:

The four quadrants are numbered from I to IV beginning with the upper right quadrant and going counterclockwise. Quadrant IV comprises the points with positive x-coordinate and negative y-coordinate, such as the point (4, -7 ) ; this is the correct quadrant.

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Example Question #4 : Points And Coordinates

Which of the following points occurs on the line given by

y=-6x+36

Possible Answers:

(12,4)

(6,0)

(0,0)

(-6,-72)

Correct answer:

(6,0)

Explanation:

Which of the following points occurs on the line given by

y=-6x+36

We can find this answer by plugging in our points one by one and finding which point "fits."

Given these points:

(12,4)

(0,0)

(-6,-72)

(6,0)

Now, we could plug in each point and be super methodical, or we could use a little strategy. On most tests, you will have a time limit. To make the most of your time, start with the easier options.

In this case, try the options with zeroes first. Zeroes tend to cancel things out quickly, and thus are easy to work with. Let's test (0,0)

$0=-6(0)+36 \rightarrow 0\neq 36$

So, (0,0) is out.

Next, try (6,0)

$0=-6(6)+36 \rightarrow 0= -36+36 \rightarrow 0=0$

So, (6,0) is our answer.

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Example Question #1 : Slope

Which of the following equations has as its graph a line with slope $\frac{1}{9 }$ ?

Possible Answers:

x+ 9 y = 81

x = 9 y + 81

9x = y + 81

9x+ y = 81

Correct answer:

x = 9 y + 81

Explanation:

For each equation, solve for and express in the slope-intercept form y=mx + b . The coefficient of will be the slope.

9x+ y = 81

9x+ y -9x = 81 -9x

y = -9x + 81

m = -9

x+ 9 y = 81

x+ 9 y - x = 81 - x

9 y = - x + 81

$\frac{9 y}{9} = \frac{ - x + 81 }{9}$

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

$m = - \frac{1}{9}$

x = 9 y + 81

9x - 81 = y + 81 - 81

y = 9x - 81

m = 9

x = 9 y + 81

x - 81= 9 y + 81 - 81

x - 81= 9 y

$\frac{x - 81}{9}= \frac{9 y }{9}$

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

$m= \frac{ 1}{9}$

x = 9 y + 81 is graphed by a line with slope $m= \frac{ 1}{9}$ and is the correct choice.

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Example Question #2 : Slope

Find the slope of -2x+2y=1 .

Possible Answers:

-1/2

Correct answer:

Explanation:

The equation given should be written in slope-intercept form, or y=mx+b format.

The in the slope-intercept equation represents the slope.

-2x+2y=1

Add on both sides of the equation.

2y = 2x + 1

Divide by two on both sides of the equation to isolate y.

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

Therefore, the slope is 1.

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Example Question #2 : Slope

Determine the slope, given the points (1,-5) and (-6,4) .

Possible Answers:

$-\frac{9}{7}$

$-\frac{1}{5}$

$-\frac{9}{5}$

$-\frac{7}{9}$

$-\frac{1}{7}$

Correct answer:

$-\frac{9}{7}$

Explanation:

Write the formula for the slope.

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

We can select any point to be (x_1, y_1) and vice versa.

$m = \frac{4-(-5)}{-6-1} = -\frac{9}{7}$

The answer is: $-\frac{9}{7}$

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Example Question #1 : Slope

Find the slope of the equation: -7x = -9y-x

Possible Answers:

$\frac{9}{7}$

$\frac{1}{3}$

$\frac{2}{3}$

$-\frac{8}{9}$

$\frac{8}{9}$

Correct answer:

$\frac{2}{3}$

Explanation:

We will need to group the x variables on one side of the equation and the y-variable on the other.

Add on both sides.

-7x+(9y) = -9y-x+(9y)

-7x+9y = -x

Add on both sides.

-7x+9y+(7x) = -x+7x

9y = 6x

Divide both sides by 9.

$\frac{9y }{9}=\frac{ 6x}{9}$

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

The slope is $\frac{2}{3}$ .

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Example Question #1 : Slope

What is the slope of the following line? -y= -2y-x

Possible Answers:

$\frac{1}{2}$

$\frac{1}{3}$

Correct answer:

Explanation:

To find the slope, rewrite the equation in slope intercept form.

y=mx+b

Add on both sides.

-y+(2y)= -2y-x +(2y)

y=-x

This is the same as: y=-1x+0

This means that the slope is .

The answer is:

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Example Question #2 : Slope

What is the slope of the following equation? y=-3(3x)-x+2

Possible Answers:

Correct answer:

Explanation:

Simplify the equation so that it is in slope-intercept format.

y=mx+b

y=-9x-x+2 = -10x+2

The simplified equation is: y=-10x+2

The slope is:

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Example Question #5 : Slope

What is the slope between the points (4,5) and (9,-10) ?

Possible Answers:

$\frac{-15}{13}$

$\frac{-1}{3}$

$\frac{15}{4}$

$\frac{13}{-15}$

Correct answer:

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:

$\frac{-10-5}{9-4}=\frac{-15}{5}=-3$

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Example Question #1 : Slope

What is the slope of the line defined as 3x+4y=10 ?

Possible Answers:

$\frac{4}{3}$

$\frac{-3}{4}$

$\frac{-1}{3}$

Correct answer:

$\frac{-3}{4}$

Explanation:

There are two ways that you can do a problem like this. First you could calculate the slope from two points. You would do this by first choosing two values and then using the slope formula, namely:

$\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}$

This could take some time, however. You could also solve it by using the slope intercept form of the equation, which is:

y=mx+b

If you get your equation into this form, you just need to look at the coefficient . This will give you all that you need for knowing the slope.

Your equation is:

3x+4y=10

What you need to do is isolate :

4y=10-3x

Notice that this is the same as:

4y=-3x+10

The next operation confuses some folks. However, it is very simple. Just divide everything by . This gives you:

$y=\frac{-3}{4}x+\frac{10}{4}$

You do not need to do anything else. The slope is $\frac{-3}{4}$ .

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GED Math : Geometry and Graphs

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #2 : Coordinate Geometry

Example Question #4 : Points And Coordinates

Example Question #1 : Slope

Example Question #2 : Slope

Example Question #2 : Slope

Example Question #1 : Slope

Example Question #1 : Slope

Example Question #2 : Slope

Example Question #5 : Slope

Example Question #1 : Slope

All GED Math Resources

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