Lesson 3.2 Rate of Change and Slope

Lesson 3.2 Rate of Change and Slope

Rate of Change

• a ratio of the amount of change in the dependent variable, or output,(y) to the amount of change in the independent variable, or input (x)

•  rates of change can be constant (always the same) or variable (changing).

You can find the rate of change using a table:

• Find the change in the dependent variable (y)

• Find the change in the independent variable (x)

• Divide the 

   $\frac{change\ in\ y}{change\ in\ x}$  

• Since all of the rates of change are the same (15), the rate of change= 15 and is constant

Multiple Choice

The table shows the approximate height of a football after it is kicked. Tell whether the rates of change are constant or variable. Find the rates of change in ft/s:

• 9

• 13

• -2.5

• 9, 13, -2.5

Multiple Choice

The rates of change are

• constant

• variable

Multiple Choice

What is the rate of change?

• 1/3

• 3

• -1/3

• -3

Multiple Choice

Tell whether the rates of change are constant or variable

• variable

• constant

Multiple Choice

What is the rate of change?

• 1 3/5

• 3

• 3, 1 3/5, 3 2/11

• 3 2/11

Multiple Choice

Is the rate of change constant or variable?

• constant

• variable

Use a graph to find rates of change.

• The graph forms a straight line, so you know it is linear and the rate of change will be the same. Choose two points on the line. (1, 15) and (2, 30)

• Find the change in y-values (rise =y₂ -y₁) 30-15= 15 and the change in x-values (run = x₂- x₁ ) 2-1=1 as you move from one point to the other.

• Divide: 15/1 = 15

• The rate of change is 15 and constant.

Calculating Slope, m 

• When the rate of change of a relationship is constant, any segment of its graph has the same steepness. The constant rate of change is called the slope of the line.

• The slope of a line is the ratio of the change in y-values (rise) for a segment of the graph to the corresponding change in x-values (run). The rise is 2. The run is -3. (Any time you move to the left, you will have a negative number)

•  $\frac{2}{-3}=\ -\ \frac{2}{3}$  so the slope is  $-\frac{2}{3}$  

• 
  

Multiple Choice

The graph shows the rate at which water is leaking from a tank. The slope of the line gives the leaking rate in gallons per minute. Find the slope of the line.

• 4/3

• 4

• 3

• 3/4

Multiple Choice

Find the slope of the line.

• 1/2

• -1/2

• 2

• -2

Multiple Choice

Find the slope of the line

• 3/2

• -3/2

• 2/3

• -2/3