1. Chapter 6 Linear Equations and Their Graphs
6.1 Rate of Change and Slope
* To find rate of change from tables and graphs
* To find slope

2. Rate of Change
Allows us to see the relationship between two quantities that are changing
Rate of Change = change in the dependent variable (y)
change in the independent variable (x)

3. What does the rate of change represent??
From a Table
For the data in the table, is the rate of change for each pair of consecutive days the same?
What does the rate of change represent??
Number of Days
Rental Charge 1
$60 2
$75 3
$90 4
$105 5
$120
Use day 5 and day 2 to find the rate of change

4. From a Graph
The graph shows the altitude of an airplane as it comes in from a landing. Find the rate of change. What does the rate of change mean?

5. SLOPE!!!! Slope = vertical change = rise horizontal change run
where x2 – x1 ≠ 0

6. Find the slope (-2, 5) (5, 12) (4, -2) (-3, 7) (5, -8) (5, -6)
(3, -2) (-9, -2)

7. Types of Slope Positive Negative Zero (0 in the numerator)
Rising Left to Right
Negative
Falling Left to Right
Zero (0 in the numerator)
Horizontal Line
Undefined (0 in the denominator)
Vertical Line

8. Finding Slope From a Graph
Remember that slope is

9. Using Slope
Through the given point, draw the line with the given slope.
K (3, 5) slope -2
S(-2, 4) slope 3/4

10. Using Slope
Each pair of points lies on the same line with the given points. Find x.
(2, 4) (x, 8) ; slope = -2
(x, 3) (2, 8) ; slope = -5/2