Question

Elizabeth's cell phone plan lets her choose how many minutes are included each month. The table shows the plan's monthly cost y for a given number of included minutes X. Write an equation in slope- intercept form to represent the situation. 100 200 300 400 500 Minutes included, x Cost of plan ($), y 14 20 26 32 38

Answer 1

$y=\frac{3x}{50}+8$

Explanation

Step 1

select two points from the table

Let

P1(100,14) and P2(200, 20)

Step 2

find the slope using

$\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2_{}-x_1}_{} \\ \text{where (x}_1,y_1)and(x_2,y_2\text{) are the coordinates of the knownpoitns} \end{gathered}$

replace,

$\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1}_{} \\ \text{slope}=\frac{20-14}{200-100}=\frac{6}{100}=\frac{3}{50}_{} \end{gathered}$

Step 3

use the slope-point equation, P1 and slope

$\begin{gathered} y-y_0=slope(x-x_0) \\ y-14=\frac{3}{50}(x-100) \\ y=\frac{3x}{50}-\frac{300}{50}+14 \\ y=\frac{3x}{50}-6+14 \\ y=\frac{3x}{50}+8 \\ \end{gathered}$