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 280 280 minutes on the phone, and paid $30.20 $ 30.20 . In another month, you spent 310 310 minutes on the phone, and paid $32.15 $ 32.15 . 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.

Respuesta :

Answer:

[tex]y = 0.065x +12[/tex]

Step-by-step explanation:

Given

[tex]x \to minutes[/tex]

[tex]y \to bill[/tex]

[tex](x_1,y_1) = (280,30.20)[/tex]

[tex](x_2,y_2) = (310,32.15)[/tex]

Required

The linear function

Start by calculating the slope (m)

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

So, we have:

[tex]m = \frac{32.15 - 30.20}{310 - 280}[/tex]

[tex]m = \frac{1.95}{30}[/tex]

[tex]m = 0.065[/tex]

The equation is then calculated as:

[tex]y = m(x - x_1) + y_1[/tex]

Where:

[tex](x_1,y_1) = (280,30.20)[/tex]

[tex]m = 0.065[/tex]

So, we have:

[tex]y = 0.065(x - 280) + 30.20[/tex]

[tex]y = 0.065x - 18.2 + 30.20[/tex]

[tex]y = 0.065x +12[/tex]