Question

Solve. Assume the exercise describes a linear relationship.

When making a telephone call using a calling card, a call lasting 3 minutes costs $1.05. A call lasting 12 minutes costs $2.85. Let y be the cost of making a call lasting x minutes using a calling card. Write a linear equation that models the cost of making a call lasting x minutes.


a. y = -0.2x + 1.65
b. y = 0.2x - 9.15
c. y = 0.2x + 0.45
d. y = 5x - 279/20

Answer 1

So, what they are saying is basically that y will be a function of x (y = f(x)) and that x is going to be the amount of time on the phone, and y is going to be the cost. So, essentially, cost is a function of time.
They also tell you that this relationship is linear. Knowing this, you can conclude that it will for sure be in this form
y = mx + b
So, you have to find m and you have to find b.
Here is what they tell you in mathematical terms:
f(3) = 1.05
f(12) = 2.85
They give you two points on the line. With two points on a line, you can always directly find the slope.
m = rise/run = (y-y0)/(x-x0) = (2.85-1.05)/(12-3) = 1.8/9 = 1/5
m = 1/5
Now, choose either of the "points" that you were given along with your slope "m" to find out what b is.
2.85 = (1/5)*12 + b
Now you can solve for b and then you have the entire linear equation.

Answer 2

I got this
y = -0.2x + 1.65

Answer 3

That's not the right answer. Probably just a calculation error if you understood the theory I posted. One other reason you know that answer doesn't make sense is because the slope is negative. If the slope were negative, that would imply that cost is decreasing as the amount of time you talk on the phone increases.

Answer 4

Oh okay let me try again.