SLOPESLOPE

What does slope What does slope measure?measure?Slope measures the steepness of

a line.

What are the different types What are the different types of slope?of slope?Positive Negative

What are the different types What are the different types of slope? (continued)of slope? (continued)Zero Undefined

Formulas to find slopeFormulas to find slope

Slope = RISERUN

Vertical ChangeHorizontal

Change

=Change in yChange in x

What is slope?What is slope?Slope is the rate of change of a

line.How would you make a graph

based on the following story problem?◦In 1970 there were 160 African

American women in elected public office in the United States. By 1993 the number had increased to 2332.

African American Women in African American Women in GovernmentGovernment

Years1970 1993

Num

ber

of

Wom

en

How do we find the actual How do we find the actual slope of this line?slope of this line? In 1970 there were

160 African American women in elected public office in the United States. By 1993 the number had increased to 2332.

What two points can we use plot the line on the coordinate plane?

We have:◦ (1970, 160)◦ (1993, 2332)

This is how we knew to put years on the x-axis and number of women on the y-axis.

Finding the slope when given Finding the slope when given two pointstwo points We established

these points:◦ (1970, 160)◦ (1993, 2332)

Our equation would be:

2332-1601993-1970

2172 or ≈ 9423

Change in yChange in x

yy22 –– yy11 xx22 –– xx11

In conclusion…In conclusion…This means that

each year between 1970 and 1993, approximately 94 more African American women worked in government.

The rate of change was….

Practice ProblemPractice ProblemFind the slope

between the following two points on a line:

(–2, –3) and (4, 6)

(x1, y1) is (–2, –3) and (x2, y2) is (4, 6)

6-(-3) = 9

4-(-2) = 6

9/6 = 3/2

Slope of the line with points (-2, -3) and (4, 6) is 3/2.

Key VocabularyKey VocabularySlopeWe use the

variable “m” to identify slope in the equation of a line.

What is slope?

Y-interceptThis is the point

at which the line crosses the y-axis.

We use the variable “b” to identify the y-intercept in the equation of a line.

Equation in “Equation in “slope-intercept slope-intercept form”form”

y = mx + b

A point on the line

Practice ProblemPractice ProblemName the slope

and y-intercept of the graph to the right.

m = 9/4b = 8

Equation of the line:

y = 9/4x + 8

Find the slope between the Find the slope between the following pointsfollowing points

1. (-2, -2) and (-4, 1)

2. (0, 0) and (4, -2)

3. (3, -6) and (2, -1)

4. (4, 2) and (0, 5)

5. (-2, -3) and (2, 4)