1. 2.5 Model Direct Variation
Algebra II

2. “y varies directly with x”
2 variables X & Y show direct variation provided y = kx & k ≠ 0.
The non-zero constant k is called the constant of variation, & y is said to vary directly with x.
The graph of y=kx is a line thru the origin.

3. Ex. 1
Write & graph a direct variation equation that has a (-3,18) as a solution.

4. Graph the equation of the line y = 3x

5. Ex. 2 The variables x & y vary directly, when x = 4, y = 12
Ex. 2 The variables x & y vary directly, when x = 4, y = Write an equation relating x & y.
Use x & y to find the constant of variation
y = kx
12 = k4
3 = k
The direct variation equation is y = 3x
This is what you MUST write as the answer!

6. In the same direct variation equation, find y, when x=5.

7. Ex. 3
Hooke’s Law states that the distance, d a spring stretches varies directly with the force f that is applied to it.
a.) Suppose a string stretches 15 inches when a force of 9 pounds is applied. Write an equation that relates d to f.

8. Ex. 3
b.) Predict the distance that the spring will stretch when a force of 6 pounds is applied.

9. Ex. 4
The dimensions of five rectangles, each with an area of 24 square feet are given in the chart. Tell whether length & width show direct variation. If so, write an equation that relates the quantities.
Length( x) 1 2 3 4 5
Width, (y) 24 12 8 6
4.8

10. Assignment

11. Ex. 3
The number C of calories a person burns performing an activity varies directly with the time t ( in minutes) the person spends performing the activity. A 160 pound person can burn 73 Calories by dancing for 20 minutes. Write a linear model that gives C as a function of t. Then estimate how long a 160 pound person should dance to burn 438 Calories.
#64

12. Ex. 3
In 1970 there were 160 African American women in elected public office in the United States. By 1993 the number had increased to Write a linear model for the number of African American women who held office at any given time between 1970 & Then use the model to predict the number that will hold office in 2010.

13. Remember average rate of change can represent slope. (Women per Year).
m = change in women = change in years
≈ 94.4 (women per year)
Now use this as slope in your linear model.

14. y = 160 + 94.4 t y = 160 + 94.4 (40) ≈ 3936 Number of Office holders
in 1970
Average rate
Of change
Years since
1970 = + *
Number of officeholders = y (people)
Number in 1970 = (people)
Average rate of change = 94.4 (people/year)
Years since 1970 = t (years)
y = t
In 2010, 40 years from 1970, you can predict:
y = (40) ≈ 3936