Question

By your cell phone contract, you pay a monthly fee plus some money for each minute you use the phone during the month. In one month, you spent 290 minutes on the phone, and paid $22.25. In another month, you spent 360 minutes on the phone, and paid $24.00.
Let x be the number of minutes you talk over the phone in a month, and let y be your cell phone bill for that month. Use a linear equation to model your monthly bill based on the number of minutes you talk over the phone.
a. This linear model's slope-intercept equation is_____________.
b. If you spent 140 minutes over the phone in a month, you would pay________________ .
c. If in a month, you paid $26.25 of cell phone bill, you must have spent ______________minutes on the phone in that month.

Answer 1

Answer:

(a) $y = 0.025x+15$

(b) 18.5 minutes

(c) 450.4 minutes

Step-by-step explanation:

Given

$290\ minutes = \ 22.25$

$360\ minutes = \ 24.00$

Solving (a): Determine the linear equation

First, we need to calculate the slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where

$(x_1,y_1) = (290,22.25)$

$(x_2,y_2) = (360,24.00)$

So, we have:

$m = \frac{24.00 - 22.25}{360 - 290}$

$m = \frac{1.75}{70}$

Multiply through by 100

$m = \frac{1.75 * 100}{70 * 100}$

$m = \frac{175}{7000}$

Next, is to calculate the equation of the line using:

$y - y_1 = m(x - x_1)$

Recall that:

$(x_1,y_1) = (290,22.25)$

$m = \frac{175}{7000}$

$y - 22.25 = \frac{175}{7000}(x - 290)$

$y - 22.25 = \frac{175x}{7000} - \frac{175}{7000} * 290$

$y - 22.25 = \frac{175x}{7000} - \frac{50750}{7000}$

Add 22.25 to both sides

$y = \frac{175x}{7000} - \frac{5075}{700} + 22.25$

$y = \frac{175x}{7000} + \frac{-5075 + 15575}{700}$

$y = \frac{175x}{7000} + \frac{10500}{700}$

$y = 0.025x+15$

(b) Solve for y when x = 140

$y = 0.025x+15$

Substitute 140 for x

$y = 0.025 * 140 + 15$

$y = 3.5 + 15$

$y = 18.5$

(c) Solve for x when y = 26.25

$y = 0.025x+15$

Substitute 26.25 for y

$26.25 = 0.025x + 15$

Solve for 0.025x

$0.025x = 26.26 - 15$

$0.025x = 11.26$

Solve for x

$x = 11.26/0.025$

$x = 450.4\ minutes$