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GED Math : Finding Slope and Intercepts

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Example Question #1 : Finding Slope And Intercepts

Find the slope and y-intercept of the line depicted by the equation:
$\small y=-\frac{1}{3}x+7$

Possible Answers:

$\small slope=-\frac{1}{3}; y-intercept=7$

$\small slope=-3; y-intercept=\frac{1}{7}$

$\small slope=-3; y-intercept=-\frac{1}{7}$

$\small slope=-\frac{1}{3}; y-intercept=-7$

Correct answer:

$\small slope=-\frac{1}{3}; y-intercept=7$

Explanation:

The equation is written in slope-intercept form, which is:
$\small y=mx+b$

where is equal to the slope and is equal to the y-intercept. Therefore, a line depicted by the equation

$\small y=-\frac{1}{3}x+7$

has a slope that is equal to $-\frac{1}{3}$ and a y-intercept that is equal to .

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Example Question #2 : Finding Slope And Intercepts

Find the slope and y-intercept of the line that is represented by the equation $y=\frac{2}{3}x-8$

Possible Answers:

$\textup{slope = }-8\textup{, y-intercept = } \frac{2}{3}$

$\textup{slope = }\frac{3}{2}\textup{, y-intercept = }-8$

$\textup{slope = } 8\textup{, y-intercept = } \frac{2}{3}$

$\textup{slope = }\frac{2}{3}\textup{, y-intercept = }-8$

$\textup{slope = }\frac{2}{3}\textup{, y-intercept = } 8$

Correct answer:

$\textup{slope = }\frac{2}{3}\textup{, y-intercept = }-8$

Explanation:

The slope-intercept form of a line is: y=mx+b , where is the slope and is the y-intercept.

In this equation, $m \textup{ = }\frac{2}{3}$ and $y \textup{ = }-8$

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Example Question #3 : Finding Slope And Intercepts

The grade of a road is defined as the slope of the road expressed as a percent as opposed to a fraction or decimal.

A road is graded so that for every 40 feet of horizontal distance, the road rises 6 feet. What is the grade of the road?

Possible Answers:

$20 \%$

$12 \%$

$18 \%$

$15 \%$

Correct answer:

$15 \%$

Explanation:

The slope is the ratio of the vertical change (rise) to the horizontal change (run), so the slope of the road, as a fraction, is $\frac{6}{40}$ . Multiply this by 100% to get its equivalent percent:

$\frac{6}{40} \times 100 \% = 15 \%$

This is the correct choice.

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Example Question #4 : Finding Slope And Intercepts

Line

Refer to above red line. What is its slope?

Possible Answers:

$\frac{1}{2}$

$-\frac{1}{2}$

Correct answer:

Explanation:

Given two points, $(x_{1}, y_{1}), (x_{2}, y_{2})$ , the slope can be calculated using the following formula:

$m = \frac{y_{2}-y_{1}}{x_{2}-x _{1}}$

Set $x_{1}=-4, y_{1}=x_{2}= 0, y_{2}=8$ :

$m = \frac{8-0}{0-(-4)} = \frac{8}{4} = 2$

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Example Question #1 : Finding Slope And Intercepts

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

3x+2y=-6

Possible Answers:

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

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

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

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

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 #6 : Finding Slope And Intercepts

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

Possible Answers:

$\frac{31}{2}$

$\frac{1}{2}$

$\frac{-1}{2}$

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 #1 : 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:

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

y=3x-34

y=5x-15

y=9x+23

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

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 #8 : Finding Slope And Intercepts

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

Possible Answers:

$\frac{159}{5}$

$\frac{159}{2}$

No x-intercept

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 #9 : 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 #10 : 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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GED Math : Finding Slope and Intercepts

Study concepts, example questions & explanations for GED Math

All GED Math Resources

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