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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 : Slope

Find the slope of the equation: 2x-3y = 4

Possible Answers:

$\frac{1}{2}$

$-\frac{3}{2}$

$\frac{2}{3}$

$-\frac{3}{4}$

$\frac{4}{3}$

Correct answer:

$\frac{2}{3}$

Explanation:

To determine the slope, we will need the equation in slope-intercept form.

y=mx+b

Subtract from both sides.

2x-3y -2x= 4-2x

-3y = -2x+4

Divide by negative three on both sides.

$\frac{-3y }{-3}= \frac{-2x+4}{-3}$

$y=\frac{2}{3}x-\frac{4}{3}$

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

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Example Question #2 : Slope

What is the slope of the line defined as 11x-44y=10 ?

Possible Answers:

$\frac{1}{4}$

$\frac{-1}{4}$

Cannot be computed from the data provided

Correct answer:

$\frac{1}{4}$

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:

11x-44y=10

What you need to do is isolate :

-44y=10-11x

Notice that this is the same as:

-44y=-11x+10

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

$y=\frac{-11}{-44}x+\frac{10}{-44}$

Now, take the coefficient from . It is $\frac{-11}{-44}$ .

You can reduce this to $\frac{1}{4}$ . This is your slope.

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Example Question #731 : Geometry And Graphs

Find the slope of the following line:

y = -8x+12

Possible Answers:

Correct answer:

Explanation:

To find the slope of a line, we will look at the line in slope-intercept form:

y=mx+b

where m is the slope and b is the y-intercept.

Now, given the line

y = -8x+12

we can see that .

Therefore, the slope of the line is -8.

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Example Question #732 : Geometry And Graphs

Line

Give the slope of the above line.

Possible Answers:

$-\frac{3}{5}$

$\frac{5}{3}$

$\frac{3}{5}$

$-\frac{5}{3}$

Correct answer:

$-\frac{5}{3}$

Explanation:

The slope of a line is defined to be the ratio of rise (vertical change, or change in the value of ) to run (horizontal change, or change in the value of ).

The -intercept of the line can be seen to be at the point five units above the origin, which is (0, 5) . The -intercept is at the point three units to the right of the origin, which is (3,0) . From these intercepts, we can find slope by setting b= 5,a = 3 in the formula

$m = - \frac{b}{a}$

The slope is

$m = - \frac{5}{3}$

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Example Question #11 : Slope

What is the slope of the following line? 6x +y-3=-2x-3

Possible Answers:

Correct answer:

Explanation:

Rearrange the terms so that it's in slope-intercept form.

y=mx+b

The slope is the . Add three on both sides.

6x +y-3 +(3)=-2x-3+(3)

6x +y = -2x

Subtract from both sides.

6x +y -6x = -2x-6x

y=-8x

The answer is:

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Example Question #733 : Geometry And Graphs

Determine the slope of the line: -y-x = -6x+2

Possible Answers:

$-\frac{6}{5}$

$-\frac{5}{2}$

Correct answer:

Explanation:

The equation will need to be rearranged to slope-intercept form.

y=mx+b

Add on both sides.

-y-x +(y)= -6x+2+(y)

-x = -6x+2+y

Subtract two on both sides, and add on both sides to isolate the variable.

-x +[6x]-(2)= -6x+2+y+[6x]-(2)

Combine like-terms.

y=5x-2

The slope is the coefficient .

The answer is:

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Example Question #11 : Slope

Determine the slope of the following line: y-3= 3(-2x+3)

Possible Answers:

$-\frac{2}{3}$

Correct answer:

Explanation:

The following equation is NOT in the proper point-slope format:

y-y_1 = m(x-x_1)

Simplify the equation by expanding the right side.

y-3= 3(-2x)+3(3)

y-3=-6x+9

Add 3 on both sides.

y-3+3=-6x+9+3

y=-6x+12

The equation is now in slope-intercept format.

y=mx+b

The slope is .

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Example Question #734 : Geometry And Graphs

Given the points (-1,-2) and (8,-13) , what is the slope of the line connecting the two points?

Possible Answers:

$-\frac{3}{2}$

$-\frac{11}{9}$

$-\frac{9}{11}$

$-\frac{7}{11}$

$\frac{15}{7}$

Correct answer:

$-\frac{11}{9}$

Explanation:

Write the formula for slope.

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

$m =\frac{-13-(-2)}{8-(-1)} = \frac{-11}{9}$

The slope is: $-\frac{11}{9}$

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Example Question #11 : Slope

Find the missing x-coordinate of the point (x, 8) if it lies on a line with (-3, 2) with a slope of $\frac{3}{5}$ .

Possible Answers:

Correct answer:

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 solve for .

$\frac{8-2}{x-(-3)}=\frac{3}{5}$

$\frac{6}{x+3}=\frac{3}{5}$

3(x+3)=30

x+3=10

x=7

The missing x-coordinate is .

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Example Question #12 : Slope

What is the slope of the following line? y= 6x+9y

Possible Answers:

$-\frac{3}{4}$

$\frac{3}{4}$

$\frac{3}{5}$

$-\frac{3}{5}$

Correct answer:

$-\frac{3}{4}$

Explanation:

The equation is not in slope-intercept form: y=mx+b

Rearrange the terms so that it is in that form.

Subtract on both sides.

y-9y= 6x+9y-9y

-8y = 6x

Divide by negative 8 on both sides.

$\frac{-8y}{-8} = \frac{6x}{-8}$

Simplify both fractions.

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

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 : Slope

Example Question #2 : Slope

Example Question #731 : Geometry And Graphs

Example Question #732 : Geometry And Graphs

Example Question #11 : Slope

Example Question #733 : Geometry And Graphs

Example Question #11 : Slope

Example Question #734 : Geometry And Graphs

Example Question #11 : Slope

Example Question #12 : Slope

All GED Math Resources

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