1. 2.4 Linear Functions and Slope
Data presented in a visual form as a set of point is called a ______________ plot.
A line that best fits the data points in a scatter plot is called a _______________ line.

2. Slope-intercept form:
y = mx + b
m is the _______________
b is the _______________
f(x) = mx + b is a linear ______________

3. Standard Form: Ax + By = C; A, B, and C are integers.
An _______________ of a graph is the
x-coordinate of a point where the graph intersects the x-axis. (a, 0)
A _______________ of a graph is the y-coordinate of a point where the graph intersects the y-axis. (0, b)

4. Example 1:
Graph using intercepts:
3x – 2y = 6

5. The measure of how steep a line is, is called ______________.
Slope compares the vertical change (the _______________) to the horizontal change (the _________________) when moving from one fixed point to another along the line.

6. Slope: Slope = change in y = Δy change in x Δx Slope = rise run
Slope = y2 – y1
x2 – x1

7. Example 2:
Find the slope of the line passing through each pair of points:
A) (-3, 4) and (-4, -2)

8. Example 2 continued . . .
B) (4, -2) and (-1, 5)

9. Positive Slope:

10. Negative Slope:

11. Zero Slope:

12. Undefined Slope:

13. Example 3:
Give the slope and the y-intercept for the line whose equation is 8x – 4y = 20.

14. Example 4:
Graph the line whose equation is
y = 4x – 3.

15. Example 5:
Graph the linear function: f(x) = - 2 x 3

16. Example 6:
Graph y = 3 in the rectangular coordinate system.

17. A horizontal line is called the _______________ function.

18. Example 7: Graph the linear equation: x = -3.
(This is not a function because it does not pass the vertical line test – it is a vertical line!)

19. Slope is the same thing as _______________ of change.

20. Example 8:
Use the graph in Figure 2.27 to find the slope of the line segment for the age group. Express the slope correct to two decimal places and describe what it represents.

21. Average Rate of Change:
If the graph of a function is not a straight line, the average rate of change between any two points is the slope of the line containing the two points.

22. Example 9:
Use Figure 2.29 to find the average rate of change in the drug’s concentration between 1 hour and 3 hours.

23. Example 10:
The table, page 139, shows the median age of first marriage for U.S. women. (The median age is the age in the middle when all ages of first-married women are arranged from youngest to oldest.) Figure 2.32 shows a scatter plot based on the data, as well as a line that passes through or near the four points.

24. Example 10 continued . . .
A) Use Figure 2.32 on page 139 to find a function in the form A(x) = mx + b that models the median age of first marriage for U.S. women, A(x), x years after 1990.

25. Example 10 continued . . .
B) Use the model to predict the median age of first marriage for U.S. women in 2030.

26. Homework:
Pages
1-81 every other odd
21 total