Graphing Lines

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Pre-Algebra › Graphing Lines

Questions 1 - 10

1

What is the slope of a line that is perpendicular to ?

$m=-\frac{1}{44}$

Explanation

The slope of a perpendicular lines has the negative reciprocal of the slope of the original line.

If an equation is in slope-intercept form, , we use the from our equation as our original slope.

In this case

First flip the sign

To find the reciprocal you take the integer and make it a fraction by placing a over it. If it is already a fraction just flip the numerator and denominator.

Do this to make the slope

$m=-\frac{1}{44}$

The slope of the perpendicular line is

$m=-\frac{1}{44}$ .

2

What is the slope of the line with the equation ?

Explanation

In the standard form equation of a line, , the slope is represented by the variable .

In this case the line has a slope of .

Therefore the answer is .

3

Find the y-intercept in the following equation:

Explanation

To find the y-intercept, we must first write the equation in y-intercept form

where b is the y-intercept. So,

we must solve for y. We must divide each term by 3. We get

$\frac{3y}{3} = \frac{9x}{3} - \frac{27}{3}$

Therefore, the y-intercept is -9.

4

and are two points on a line. What is the slope of this line?

$\frac{1}{2}$

Explanation

The slope of the line is determined by $\frac{rise}{run}$ . In other words, we can use the formula $\frac{y_2-y_1}{x_2-x_1}$ .

Let's choose the coordinate to be ( , ) and to be ( , ).

We can now use the formula above:

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

5

What is the slope and y-intercept of the equation

$y = \frac{1}{4}x -5\textup{ ?}$

$\textup{slope} = \frac{1}{4}$

$\textup{y-intercept} = -5$

$\textup{slope} = -5$

$\textup{y-intercept} = \frac{1}{4}$

$\textup{slope} = \frac{1}{4}$

$\textup{y-intercept} = 5$

$\textup{slope} = \frac{1}{4}x$

$\textup{y-intercept} = -5$

$\textup{slope} = -5$

$\textup{y-intercept} = \frac{1}{4}x$

Explanation

The slope intercept formula is:

6

Find the y-intercept of the following equation of a line:

Explanation

To find the y-intercept of an equation, we must first write it in slope-intercept form

where m is the slope and b is the y-intercept. So, in our equation of a line, we must solve for y.

We must divide each term by 3.

$\frac{3y}{3} = \frac{-12x}{3} + \frac{36}{3}$

where -4 is the slope and 12 is the y-intercept.

Therefore, the y-intercept is 12.

7

What is the slope and y-intercept of the equation below?

$y= -\frac{1}{2}x -8$

Slope = $-\frac{1}{2}$

Y-intercept =

Slope = $\frac{1}{2}x$

Y-intercept =

Slope = $-\frac{1}{2}$

Y-intercept =

Slope = $-\frac{1}{2}x$

Y-intercept =

Slope = $\frac{1}{2}$

Y-intercept =

Explanation

In order to understand this question you must understand what slope intercept form is.

= slope

= y-intercept

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

The y-intercept is

8

Which of the follow lines is parallel to:

$y=\frac{1}{14}x+9$

$y=\frac{-1}{14}x+9$

Cannot be determined

Explanation

It is known that parallel lines have the same slope and therefore a line that is parallel to:

MUST have the same slope of .

9

What is the slope of the line ?

Explanation

In the slope-intercept form of a line, , the slope is represented by the variable .

In this case the line

has a slope of .

The answer is .

10

What is the slope-intercept form of a line?

Explanation

The slope-intercept form of a line is .

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