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.

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

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)

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

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.

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

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

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

Positive Slope:

Negative Slope:

Zero Slope:

Undefined Slope:

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

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

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

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

A horizontal line is called the _______________ function.

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!)

Slope is the same thing as _______________ of change.

Example 8: Use the graph in Figure 2.27 to find the slope of the line segment for the 50-59 age group. Express the slope correct to two decimal places and describe what it represents.

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.

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

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.

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.

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

Homework: Pages 140-142 1-81 every other odd 21 total