Finding Slope and Intercepts

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GED Math › Finding Slope and Intercepts

Questions 1 - 10

1

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

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

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

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

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

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 .

2

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

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

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

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

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

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

Explanation

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

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

3

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

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

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

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

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

Explanation

Convert the equation into slope-intercept form, which is , where is the slope and is the y-intercept.

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

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

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

4

Identify the y-intercept:

$\textup{No solution.}$

$\frac{3}{2}$

$\frac{2}{3}$

Explanation

In order to find the y-intercept, we will need to let and solve for .

Subtract from both sides. Do NOT divide by on both sides.

The answer is:

5

What is the slope of the following equation?

$\frac{1}{2}$

$-\frac{1}{2}$

Explanation

Rewrite the equation in slope-intercept format:

Divide both sides by two.

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

The slope is .

6

What is the y-intercept of the following line:

Explanation

To find the y-intercept, we will write the equation in slope-intercept form

where b is the y-intercept.

So, given the equation of the line

we will solve for y. We get

$\frac{9y}{9} = \frac{18x}{9} + \frac{27}{9}$

Therefore, the y-intercept of the equation is 3.

7

Find the slope of the following function:

Explanation

Simplify the terms of the equation by distribution.

Subtract the terms.

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

The slope is .

The answer is .

8

What is the x-intercept of ?

$\frac{159}{5}$

$\frac{159}{2}$

No x-intercept

Explanation

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

Simply solving, this is

9

Line

Refer to above red line. What is its slope?

$\frac{1}{2}$

$-\frac{1}{2}$

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

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

10

What is the slope of the following equation?

$\frac{19}{8}$

$\frac{8}{19}$

Explanation

The equation is already given in slope-intercept form:

The is the slope, and the represents the y-intercept.

The answer is:

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