Linear Functions 2 — Heart of Algebra

Questions in this quiz (10)

1. A streaming service charges a one-time activation fee and a monthly subscription fee. The total cost, $$C(m)$$, in dollars, after $$m$$ months is modeled by $$C(m)=4.75m+18$$ Which of the following is the best interpretation of $$4.75$$ in this context?

   • The one-time activation fee, in dollars
   • The total cost, in dollars, after $$4.75$$ months
   • The monthly subscription fee, in dollars per month
   • The maximum number of months a customer can subscribe

2. A bike rental company charges a fixed rental fee of $$8$$ dollars and an additional $$3.75$$ dollars for each hour the bike is rented. Let $$t$$ represent the number of hours rented. Which equation defines $$f$$, where $$f(t)$$ is the total cost, in dollars, for renting the bike for $$t$$ hours?

   • $$f(t)=8t+3.75$$
   • $$f(t)=3.75t+8$$
   • $$f(t)=11.75t$$
   • $$f(t)=3.75t-8$$

3. In the $$xy$$-plane, the graph of the linear function $$f$$ contains the points $$(-2,-7)$$ and $$(6,25)$$. Which equation defines $$f$$, where $$y=f(x)$$?

   • $$f(x)=4x+1$$
   • $$f(x)=5x+3$$
   • $$f(x)=4x-7$$
   • $$f(x)=3x+1$$

4. A fitness center offers a membership plan where the total cost, $$C(m)$$, in dollars, is a linear function of the number of months $$m$$ a person is a member. The cost includes a one-time enrollment fee and a monthly charge. If the total cost for $$8$$ months is $$420$$ and the total cost for $$14$$ months is $$690$$, what is the one-time enrollment fee?

   • $$40$$
   • $$50$$
   • $$60$$
   • $$80$$

5. A truck begins a trip with a certain amount of fuel in its tank. After driving $$80$$ miles, it has $$18$$ gallons of fuel remaining. After driving a total of $$280$$ miles, it has $$10$$ gallons remaining. Assume fuel is consumed at a constant rate. Which equation represents the amount of fuel, $$y$$, in gallons, remaining after driving $$x$$ miles?

   • $$y=-\frac{1}{25}x+\frac{106}{5}$$
   • $$y=-\frac{1}{20}x+22$$
   • $$y=\frac{1}{25}x+\frac{106}{5}$$
   • $$y=-\frac{1}{25}x+18$$

6. A line in the $$xy$$-plane passes through the points $$(-3,-8)$$ and $$(7,22)$$. What is the $$y$$-coordinate of the point where this line intersects the $$y$$-axis?

   • $$1$$
   • $$2$$
   • $$3$$
   • $$4$$

7. In the $$xy$$-plane, line $$k$$ is perpendicular to the line represented by the equation $$5x-2y=20$$ and passes through the point $$(4,-3)$$. What is the $$y$$-intercept of line $$k$$?

   • $$(0,-\frac{7}{5})$$
   • $$(0,7)$$
   • $$(0,5)$$
   • $$(0,3)$$

8. If a line has a slope of $$-\frac{2}{5}$$ and passes through the point $$(3,4)$$, which of the following points also lies on the line?

   • $$(-2,6)$$
   • $$(8,2)$$
   • $$(13,0)$$
   • $$(8,6)$$

9. A telecommunications company offers two different monthly phone plans, Plan A and Plan B. The total monthly cost, $$y$$, in dollars, for using $$x$$ gigabytes of data is represented by a linear equation for each plan.Plan A: $$y=8x+20$$Plan B: $$y=2x+50$$The graph shows the cost of each plan based on the amount of data used. What does the point $$(5,60)$$ on the graph represent in this context?

   • The cost of Plan A is $$\$60$$ when $$5$$ gigabytes of data are used.
   • The cost of Plan B is $$\$5$$ when $$60$$ gigabytes of data are used.
   • Both plans cost $$\$60$$ when $$5$$ gigabytes of data are used.
   • The difference in cost between Plan A and Plan B is $$\$5$$ when $$60$$ gigabytes are used.

10. A coffee shop sells two sizes of coffee: small and large.- A small coffee costs $$\$2.50$$.- A large coffee costs $$\$4.00$$.- A total of $$150$$ coffees were sold.The relationship between the total revenue, $$R$$, in dollars, and the number of small coffees sold, $$s$$, can be represented by a linear equation. Which of the following equations correctly represents this relationship?

    • $$R=2.50s+4.00s$$
    • $$R=4.00s+2.50(150-s)$$
    • $$R=600-1.50s$$
    • $$R=600+1.50s$$