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

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)

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

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?

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

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

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

Finding Slope From a Graph Remember that slope is

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

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