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GED Math : GED Math

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

Example Questions

Example Question #3 : Finding Slope And Intercepts

What is the slope and y-intercept of the following line?

3x+2y=-6

Possible Answers:

$m=-\frac{3}{2};b=-3$

$m=\frac{2}{3};b=-3$

$m=-\frac{2}{3};b=3$

$m=-3;b=\frac{3}{2}$

Correct answer:

$m=-\frac{3}{2};b=-3$

Explanation:

Convert the equation into slope-intercept form, which is y=mx+b , where is the slope and is the y-intercept.

3x+2y=-6

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

2y=-6-3x

$\frac{2y}{2}=\frac{-6-3x}{2}$

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

$m=-\frac{3}{2}$

b=-3

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Example Question #5 : Finding Slope And Intercepts

What is the slope of the line perpendicular to 3x + 6y=93 ?

Possible Answers:

$\frac{1}{2}$

$\frac{31}{2}$

$\frac{-1}{2}$

Correct answer:

Explanation:

In order to find the perpendicular of a given slope, you need that given slope! This is easy to compute, given your equation. Just get it into slope-intercept form. Recall that it is y=mx+b

Simplifying your equation, you get:

6y=-3x+93

$y=\frac{-1}{2}x+\frac{93}{6}$

This means that your perpendicular slope (which is opposite and reciprocal) will be .

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Example Question #6 : Finding Slope And Intercepts

What is the equation of a line with a slope perpendicular to the line passing through the points (2,4) and (7,19) ?

Possible Answers:

y=5x-15

$y=\frac{-1}{3}x+94$

y=3x-34

$y=\frac{-1}{5}x+17$

y=9x+23

Correct answer:

$y=\frac{-1}{3}x+94$

Explanation:

First, you should solve for the slope of the line passing through your two points. Recall that the equation for finding the slope between two points is:

$\frac{rise}{run} = \frac{y_2-y_1}{x_2-x1}$

For your data, this is

$\frac{19-4}{7-2}=\frac{15}{5}=3$

Now, recall that perpendicular slopes are opposite and reciprocal. Therefore, the slope of your line will be $\frac{-1}{3}$ . Given that all of your options are in slope-intercept form, this is somewhat easy. Remember that slope-intercept form is:

y=mx+b

is your slope. Therefore, you are looking for an equation with $m=\frac{-1}{3}$

The only option that matches this is:

$y=\frac{-1}{3}x+94$

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Example Question #7 : Finding Slope And Intercepts

What is the x-intercept of 2y+3x=159 ?

Possible Answers:

No x-intercept

$\frac{159}{5}$

$\frac{159}{2}$

Correct answer:

Explanation:

Remember, to find the x-intercept, you need to set equal to zero. Therefore, you get:

3x=159

Simply solving, this is x=53

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Example Question #6 : Finding Slope And Intercepts

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

Possible Answers:

$\frac {2}{3}$

$-\frac {2}{3}$

$\frac {4}{3}$

Correct answer:

$\frac {2}{3}$

Explanation:

Step 1: Move x and y to opposite sides...

We will subtract 2x from both sides...

Result, -3y=-2x+4

Step 2: Recall the basic equation of a line...

y=mx+b , where the coefficient of y is .

Step 3: Divide every term by to change the coefficient of y to :

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

Step 4: Reduce...

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

Step 5: The slope of a line is the coefficient in front of the x term...

So, the slope is $\frac {2}{3}$

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Example Question #6 : Finding Slope And Intercepts

Find the slope of the following equation: y=-9(-x+6)

Possible Answers:

$\textup{The slope cannot be determined.}$

$\frac{1}{9}$

Correct answer:

Explanation:

In order to find the slope, we will need the equation in slope-intercept form.

y=mx+b

Distribute the negative nine through the binomial.

y=(-9)(-x)+(-9)(6) = 9x-54

The slope is:

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Example Question #11 : Finding Slope And Intercepts

What is the y-intercept of the following equation? -3x= y+7

Possible Answers:

$\frac{7}{3}$

$-\frac{3}{7}$

$-\frac{7}{3}$

Correct answer:

Explanation:

The y-intercept is the value of when x=0 .

Substitute the value of zero into , and solve for .

-3(0)= y+7

0 = y+7

Subtract 7 from both sides.

0 -7= y+7-7

y=-7

The answer is:

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Example Question #11 : Finding Slope And Intercepts

Find the slope and y-intercept, respectively, given the following equation:

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

Possible Answers:

$-\frac{2}{3}, \frac{1}{2}$

$\frac{1}{2}, \frac{1}{3}$

$\frac{1}{2}, -\frac{1}{3}$

$-\frac{1}{2}, -\frac{1}{3}$

$\frac{2}{3}, \frac{1}{2}$

Correct answer:

$\frac{1}{2}, \frac{1}{3}$

Explanation:

Rewrite the equation in slope-intercept format: y=mx+b

Divide by negative two on both sides. This is also the same as multiplying both sides by negative half.

$(-2y) (-\frac{1}{2})= (-\frac{1}{2})(-\frac{2}{3}-x)$

$y = \frac{1}{3}+\frac{1}{2}x$

Rearrange the terms.

$y =\frac{1}{2}x+ \frac{1}{3}$

The slope is: $\frac{1}{2}$

The y-intercept is: $\frac{1}{3}$

The answer is: $\frac{1}{2}, \frac{1}{3}$

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Example Question #11 : Finding Slope And Intercepts

Find the slope of the following function: y=-5(-5x+2x)

Possible Answers:

Correct answer:

Explanation:

Simplify the terms of the equation by distribution.

y=-5(-5x+2x) = 25x-10x

y= 25x-10x

Subtract the terms.

y=15x

The equation is now in slope-intercept form, where b=0 .

The slope is .

The answer is .

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Example Question #11 : Finding Slope And Intercepts

What is the slope of the following equation? x+9y = -7

Possible Answers:

$-\frac{7}{9}$

$-\frac{1}{9}$

$-\frac{9}{7}$

Correct answer:

$-\frac{1}{9}$

Explanation:

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

y=mx+b

Subtract on both sides.

x+9y -x= -7-x

9y = -x-7

Divide by 9 on both sides.

$\frac{9y }{9}= \frac{-x-7}{9}$

Split both terms on the right side.

$y= -\frac{1}{9}x-\frac{7}{9}$

The slope is: $-\frac{1}{9}$

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GED Math : GED Math

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #3 : Finding Slope And Intercepts

Example Question #5 : Finding Slope And Intercepts

Example Question #6 : Finding Slope And Intercepts

Example Question #7 : Finding Slope And Intercepts

Example Question #6 : Finding Slope And Intercepts

Example Question #6 : Finding Slope And Intercepts

Example Question #11 : Finding Slope And Intercepts

Example Question #11 : Finding Slope And Intercepts

Example Question #11 : Finding Slope And Intercepts

Example Question #11 : Finding Slope And Intercepts

All GED Math Resources

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