slope. what does slope measure? slope measures the steepness of a line
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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.
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