1. Rate of Change and Slope
3-3 Notes for Algebra 1
Rate of Change and Slope

2. Rate of Change
A ratio that describes how much one quantity changes with respect to a change in another quantity. x—is the independent variable. y—is the dependent variable. 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒= 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥 A positive rate of change indicates an increase over time. A negative rate of change indicates that a quantity is decreasing.

3. Example 1 pg. 172 Find the Rate of Change
DRIVING TIME Use the table to find the rate of change. Then explain its meaning.
Time Driving
(h)
Distance
Traveled (mi) x Y 2 76 4
152 6
228

4. Example 1 pg. 172 Find the Rate of Change
DRIVING TIME Use the table to find the rate of change. Then explain its meaning ; this means the car is traveling at a rate of 38 miles per hour.
Time Driving
(h)
Distance
Traveled (mi) x Y 2 76 4
152 6
228

5. Example 2 pg. 173 Compare Rates of Change
TRAVEL The graph shows the number of
U.S. passports issued in 2002, 2004 and
1.) Find the rate of change for
and
2.) Explain the meaning of the rate of change 5
in each case
3.) How are the different rates of change shown on the graph.
12.1
8.9
7.0

6. Example 2 pg. 173 Compare Rates of Change
TRAVEL The graph shows the number of
U.S. passports issued in 2002, 2004 and
1.) Find the rate of change for
and 5
950,000/yr 1,600,000/yr
12.1
8.9
7.0

7. Example 2 pg. 173 Compare Rates of Change
TRAVEL The graph shows the number of
U.S. passports issued in 2002, 2004 and 9 7
2.) Explain the meaning of the rate of change 5
in each case
For there was an annual increase of 950,000 passports issued. Between , there was an average yearly increase of 1,600,000 passports issued.
12.1
8.9
7.0

8. Example 2 pg. 173 Compare Rates of Change
TRAVEL The graph shows the number of
U.S. passports issued in 2002, 2004 and 9 7 5
3.) How are the different rates of change shown on the graph.
There is a greater vertical change for than for Therefore, the section of the graph for is steeper.
12.1
8.9
7.0

9. Slope (m)
The slope of a non-vertical line is the ratio of the change in the y- coordinates (rise) to the change in the x-coordinates (run) 𝑠𝑙𝑜𝑝𝑒= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 𝑥 1 , 𝑦 1 , 𝑥 2 , 𝑦 2 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦−𝑐𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒𝑠 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥−𝑐𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒𝑠 = 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1

10. Example 4 pg. 175 Positive, Negative and Zero slopes
Find the slope of the line that passes through each pair of points. 1.) −3, 2 and 5, 5 2.) −3, −4 and −2, −8 3.) −3, 4 and 4, 4

11. Example 4 pg. 175 Positive, Negative and Zero slopes
Find the slope of the line that passes through each pair of points. 1.) −3, 2 and 5, 5 𝑚= ) −3, −4 and −2, −8 𝑚=−4 3.) −3, 4 and 4, 4 𝑚=0

12. Example 5 pg. 176 Undefined Slope
Find the slope of the line that passes through −2, −4 and −2, 3 .

13. Example 5 pg. 176 Undefined Slope
Find the slope of the line that passes through −2, −4 and −2, 3 . Undefined

14. Slope Summary
Positive Slope– goes uphill from left to right Negative Slope– goes downhill from left to right Slope of 0– horizontal line (y = #) Undefined Slope– vertical line (x = #)

15. Example 6 pg. 176 Find Coordinates given the slope.
Find the value of r so that the line through 6, 3 and 𝑟, 2 has a slope of

16. Example 6 pg. 176 Find Coordinates given the slope.
Find the value of r so that the line through 6, 3 and 𝑟, 2 has a slope of 𝑟=4

17. 3-3 pg o, 43-45, 54-66(x3)