Refresher Rate of Change in the Real World

Key terms

Term / Definition / Example
Rate of Change / Ratio of the change in the output value and the change in the input value of a function.
Slope

Refresher – Rate of Change in the Real World

Felipe had to go run an errand before he could head home after school. The graph below follows his journey measuring distance from school over time. Complete the table identifying the domain, change in x, range, change in y, and a sentence explaining the rate of change.
Hint: “As ___[indep. var.]____ increases by 1 unit, ___[dep. var.]___ increases/decreases by ____[rate of change]____.”
/ ∆x / ∆y / R.o.C. / Interpretation of R.o.C.
1
2
3
4

Slope

Rate of Change = ------= ------= ------= Slope

We Do – Slope from Graphs (Real World)

Example 1. The graph below shows the growth of Darin’s tree over many years. Identify the slope of the line.
What does this mean? / 2. Jeremy goes to mall and buys clothes on a spending spree of sorts. Identify the slope of the line. What does this mean?

We Do – Slope from Graphs We Do – Slope in Verbal Descriptions

Example 3. Identify the slope of the line below. / 4. Identify the slope of the line below.
/ 5. Identify the meaning of the slope in the equation:
You just adopted a baby turtle. Your turtle is growing at a constant rate. The turtle’s length, L, in inches, as a function of his age, w, in weeks, is modeled by the equation L=0.2w+3.
Meaning of the slope: / 6. Identify the meaning of the slope in the equation:
You work at Saks Fifth Avenue selling women’s shoes. Your monthly income, y, in dollars, as a function of how many shoes your customers buy, x, is modeled by the equation
y=25x+1225.
Meaning of the slope:

You Do Goal: ______%

Do at least 11 out of the 16 problems. Make sure to use resources and check your work as you go!

1.  Simplify:
26x+2y+43x+2+4y / 2. Identify the slope of the line below.

m = / 3. Identify the slope of the line below.
m = / 4. Kayla makes extra money after school by mowing her neighbors’ lawns. The time, t seconds, that it takes Kayla to mow a lawn, is a function of the lawn’s area (in square feet), a, is modeled by the function t=30a+300.
What is the slope of this equation, and what does it mean?
5. Solve: 23x-7=13 / 6. Identify the slope of the line below.

m = / 7. Identify the slope of the line below.

m = / 8. Identify the slope of the line below.
m =
9. Simplify:
2x-1-x+5-y+4y / 10. Identify the slope of the line and its meaning.
m =
Meaning: / 11. Calculate the slope from the table below.
X (days) / Y (miles I ran)
3 / 7
4 / 9
5 / 11
The amount of
______increases
by ______per
______. / 12. Identify the slope of the line and its meaning.

m =
Meaning:
13. Solve: 6x+12=0 / 14. Solve: x-2+4=10 / 15. Shari works at a car dealership. She earns a base pay, and then makes commission on each car she sells. Her annual pay, p, in dollars, is a function of how many cars she sells, c, modeled by the equation
p=3200c+17000. What is the slope of this equation, and what does it mean? / 16. Write an expression that matches the following description: “eighteen less the product of x and four.”