10 3 Slope and Rate of Change Learn

10 -3 Slope and Rate of Change Learn to find rates of change and slopes.

10 -3 Slope and Rate of Change Vocabulary rate of change slope

10 -3 Slope and Rate of Change The rate of change of a function is a ratios that compares the difference between two output values to the difference between the corresponding input values.

10 -3 Slope and Rate of Change Additional Example 1 A: Using A Table to identify Rates of Change Tell whether the rates of change are constant or variable. +2 +1 +2 +3 Find the difference x 2 4 7 8 10 between y 5 11 20 23 29 consecutive data points. +6 +3 +6 +9 Find each ratio of the change in y to the change in x. The rate of change is constant.

10 -3 Slope and Rate of Change Caution! Be careful to put the difference in y-values in the numerator and the differences in x -values in the denominator when you write a rate of change.

10 -3 Slope and Rate of Change Additional Example 1 B: Using A Table to identify Rates of Change Tell whether the rates of change are constant or +1 +1 variable. Find the difference x 0 1 2 3 4 between y 0 3 5 8 10 consecutive data points. +2 +3 +3 +1 Find each ratio of the change in y to the change in x. The rates of change are variable.

10 -3 Slope and Rate of Change Check It Out: Example 1 Tell whether the rates of change are constant or variable. +3 +1 +2 +3 Find the difference x 0 2 5 6 9 between y 5 15 30 35 50 consecutive data points. +15 +10 +15 +5 Find each ratio of the change in y to the change in x. The rate of change is constant.

10 -3 Slope and Rate of Change When the rate of change is constant, the segments form a straight line. The constant rate of change of a line is its slope.

10 -3 Slope and Rate of Change Reading Math Recall that a function whose graph is a straight line is a linear function.

10 -3 Slope and Rate of Change Additional Example 2: Driving Application The table shows the driving distances that Jesse recorded. A. Determine whether the rates of change are constant or variable. The rate of change is constant.

10 -3 Slope and Rate of Change Additional Example 2: Driving Application B. Graph the data and connect the points with line segments. If the rate of change is constant, find and interpret the slope. The rate of change between 3 any two points is 5. The slope of the line is 3. 5 The slope is 3. This means he drove 3 mi. every 5 min. 5

10 -3 Slope and Rate of Change Check It Out: Example 2 The table shows the driving distances that Barry recorded. Time (min) 1 3 6 9 12 Distance (miles) 3 6 12 18 24 Determine whether the rates of change are constant or variable. 3 =3 1 6 =2 3 12 = 2 6 18 = 2 9 The rates of change are variable. 24 = 2 12