Linear Algebra

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GED Math › Linear Algebra

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 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 .

3

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 $y \textup{ = }-8$

4

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.

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

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

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

5

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 $y \textup{ = }-8$

6

Which of the following equations is written in slope-intercept form?

$\small y=4x+2$

$\small 4x-y+2=0$

$\small 4x-y=-2$

$\small x=\frac{1}{4}y-2$

Explanation

Slope-intercept form is written as $\small y=mx+b$ .

There is only one answer choice in this form:

$\small y=4x+2$

7

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.

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

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

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

8

Which of the following equations is written in slope-intercept form?

$\small y=4x+2$

$\small 4x-y+2=0$

$\small 4x-y=-2$

$\small x=\frac{1}{4}y-2$

Explanation

Slope-intercept form is written as $\small y=mx+b$ .

There is only one answer choice in this form:

$\small y=4x+2$

9

Rewrite the following equation in slope-intercept form.

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

$x=\frac{4}{3}y-\frac{8}{3}$

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

$y=\frac{3}{4}x+32$

Explanation

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

Below are the steps to get the equation into slope-intercept form.

$2+4y=3x+10 \textup{ (Subtract 2 from both sides)}$

$4y=3x+8 \textup{ (Divide both sides by 4)}$

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

10

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:

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