SLE - Compare Linear Functions (Lesson)
Compare Linear Functions
The last module, we explored linear functions and how to graph them. When graphing a line, one of the most important features you need to know is the slope of the line! Recall, when we are finding the slope of the line, we often think of rise/run. We also referred to the slope as the rate of change.
The rate of change is found by finding the change in y/change in x and can be thought of as the rate at which a function is increasing or decreasing. Linear functions will always have a constant rate of change.
Rate of Change Practice
So let's try a few real-world examples. For each problem below, find the rate of change:
1. Turner is reading his summer novel. He has timed himself and finds that he reads 4 pages every 5 minutes. What is his rate of reading per minute?
2. The taxi cab states that it charges a $3 initial fee and $2.25 per mile. What is the rate of change of the cost of the taxi ride?
3. You run 4 miles in 1 hour and 12 miles in 3 hours. What is your speed of running?
4.
| Tickets for rides | 10 | 12 | 14 | 16 |
| Total cost of carnival ($) | $12.50 | $14.00 | $15.50 | $17.00 |
5.
| Pounds of Apples | 1 | 2 | 3 | 4 |
| Total Cost ($) | $1.49 | $2.98 | $4.47 | $5.96 |
Let's try interpreting a non-linear graph. The graph below tracks the regular gasoline prices from July 2004 to December 2004. Use this graph to answer the questions.
6. What is the slope of the line from November to December?
7. Between what months did the price not change?
8. What is the slope of the line between October and November?
9. Between what months did the price change the most?
Now let's think about comparing different linear functions to discuss which one is growing faster. As the slope of a line increases, the rate of change increases - so the greater the slope, the faster the function is growing.
In the image, you can see that the line with a slope of 3 is steeper and therefore growing faster than the line with a slope of 1.
Let's compare two different cell phone plans. The plan shown in the graph below is from Cell Town. The plan in the table is from Digital Data.
| GB of Data Used | Cost of Plan |
| 1 | 20 |
| 4 | 35 |
| 6 | 45 |
| 9 | 60 |
11. What is the rate of change for the plan from Digital Data?
12. What is the rate of change for the plan from Cell Town?
13. If you only use 4 GB of data a month, which cell phone plan is the best deal?
14. When are the two plans the same cost?
15. If you use 10 GB of data, which plan is the best deal?
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IMAGES CREATED BY GAVS