1. The cost of nails varies directly with the number of pounds bought. If 4 pounds of nails cost $11.60, what is the cost of 3.5 pounds? Write and solve a direct variation equation.
a. / y = 2.9x; $11.60b. / y2.9x; $10.15
c. / y = 3x; $10.50
d. / y = 3x; $11.75
2.A person’s body weight on the moon varies directly with the body weight on Earth, as shown in the table below.
Body Weight (lb) / 120 / 20
a. Write and graph an equation that relates the body weight on the moon, y, to body weight on Earth, x.
Equation: ______
b. Explain how the equation shows a
proportional linear relationship. ______
c. Explain how the graph shows a proportional linear relationship. ______
3. The rental fee to rent jet skis varies directly as the number of hours that you rent them. Fun Vacation Rentals rents jet skis to tourists. They charge $140 for 4 hours. Suppose you rent a jet ski for only 3 hours. Write and solve a direct variation equation to determine your rental fee.
Equation: ______
Solution: ______
4. The amount Ben earns y varies directly with the number of hours he works x as shown in the graph. Write a direct variation equation. Identify the constant of variation and interpret its meaning.
Ben works, he earns $10.
b. / y = 5.5x; ; For every hour
Ben works, he earns $5.50.
c. / y = 10x; ; For every hour Ben works, he earns $5.50.
5. Olivia is an aide at a daycare. The table shows the numbers of aides needed for certain numbers of children. Write an equation that represents the relationship between the number of children y and the number of aides x.
Equation: ______
6. The table below shows the relationship between the cost of ground turkey at a local market and the number of pounds bought. Write an equation that represents the relationship of cost, y, to the number of pounds bought, x.
Equation: ______
7. Write an equation in slope-intercept form for the table.
Equation: ______
8. Write an equation in slope-intercept form for the table.
Equation: ______
9. The entrance fee to the Houston Museum is $25. An exhibit fee is $5 per exhibit. The total cost y for the museum visit for xexhibits can be represented by the equation y = 25 + 5x.
Interpret the slope: ______
Interpret the y-intercept: ______
10. The points in the table below lie on a line. What is the value of y when x is 8?
11. At Store A, pencils are sold individually. The cost y of x pencils is represented by the equation y0.55x. The costs of pencils at Store B are shown in the table. State whether the statement is true or false. “The pencils at Store A cost more.” Explain.
a. / False; the rate of change is the same
b. / True; The rate of change in the table is 0.53. The rate of the change in the equation is 0.55. So, the rate of change at Store A is greater.
c. / True; The rate of change in the table is 0.51. The rate of the change in the equation is 0.55. So, the rate of change at Store A is greater.
12. Write the equation for the line that passes through
(0, 1) and (2, 5).
Equation: ______
13. What is the equation in slope-intercept form for the graph shown?
Equation:______
14. At Store A, balloons are sold individually. The cost y of x balloons is represented by the equation y 1.25x. The costs of balloons at Store B are shown in the table. State whether the statement is true or false. “The balloons at Store A cost more.” Explain.
a. / False; The rate of change in the table is 1.50. The rate of change in the equation is 1.25. So, the rate of change at Store B is greater.
b. / True; The rate of change in the table is 1.00. The rate of change in the equation is 1.25. So, the rate of change at Store A is greater.
c. / False; The rate of change in the table is 1.25. The rate of change in the equation is 1.25. So, the rates of change are equivalent.
d. / False; The rate of change in the table is 1.75. The rate of change in the equation is 1.25. So, the rate of change at Store B is greater.
15. The points in the table below lie on a line. What is the value of y when x is 5?
Equation ______
When x =5, y = ______
16. State the x- and y-intercepts of the line defined by the function . Graph the function.
x-intercept: ______y-intercept: ______
Graph:
17. Monty has a total of $290 in ten dollar and five dollar bills. This can be represented by the equation 10x + 5y = 290. Interpret the x- and y-intercepts.
a. / The x-intercept indicates that he has 58 ten dollar bills and no five dollar bills. The y-intercept indicates that he has 29 five dollar bills and no ten dollar bills.b. / The x-intercept indicates that he has 29 ten dollar bills and no five dollar bills. The y-intercept indicates that he has 29 five dollar bills and no ten dollar bills.
c. / The x-intercept indicates that he has 29 ten dollar bills and no five dollar bills. The y-intercept indicates that he has 58 five dollar bills and no ten dollar bills.
d. / The x-intercept indicates that he has 5 ten dollar bills and no five dollar bills. The y-intercept indicates that he has 10 five dollar bills and no ten dollar bills.
18. What is the slope and y-intercept for the graph of the equation 5x + y = -9?
m = ______b = ______
ANSWER KEY
1.B
2.a) y = 1/6x; b) y=mx form c) line passes through the origin
3.y=35x; $105
4.B
5.y=6x
6.y=3.5x
7.y= 5/6x - 3
8.y= -3x - 7
9.m= $5 per exhibit; b = $25 entrance
10.5
11. C
12.y = 2x+ 1
13.y = 3x + 2
14.A
15.9
16.x-int.= -8; y-int.=1/2
17.C
18.m = -5; b = -9