SLOPE. What does slope measure? Slope measures the steepness of a line.

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Presentation transcript:

SLOPE

What does slope measure? Slope measures the steepness of a line.

What are the different types of slope? Positive Negative

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

Formulas to find slope Slope = RISE RUN Vertical Change Horizontal Change = Change in y Change in x

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 Government Years Number of Women

How do we find the actual 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 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 two points We established these points: ◦ (1970, 160) ◦ (1993, 2332) Our equation would be: or ≈ Change in y Change in x y2 – y1y2 – y1y2 – y1y2 – y1 x2 – x1x2 – x1x2 – x1x2 – x1

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 Problem Find the slope between the following two points on a line: (–2, –3) and (4, 6) (x 1, y 1 ) is (–2, –3) and (x 2, y 2 ) 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 Vocabulary Slope We use the variable “m” to identify slope in the equation of a line. What is slope? Y-intercept This 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 “slope-intercept form” y = mx + b A point on the line

Practice Problem Name the slope and y-intercept of the graph to the right. m = 9/4 b = 8 Equation of the line: y = 9/4x + 8

Find the slope between the following 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)