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.

(a)

(b) 18.5 minutes

(c) 450.4 minutes

Step-by-step explanation:

Given

Solving (a): Determine the linear equation

First, we need to calculate the slope (m)

Where

So, we have:

Multiply through by 100

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

Recall that:

Add 22.25 to both sides

(b) Solve for y when x = 140

Substitute 140 for x

(c) Solve for x when y = 26.25

Substitute 26.25 for y

Solve for 0.025x

Solve for x

the answer is:

the correct option:

b.

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

then, using placing logarith with base 7 on both sides of the equation, we have:

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

hence, we have that the correct option:

b.

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