Question

martin just got his first cell phone from worldwide wireless. he paid worldwide wireless an activation fee to start, but the total amount he will spend on the plan depends on how long he has it. this situation can be modeled as a linear relationship. complete the statement that describes the situation. after an activation fee of, the plan will cost martin

Explanation:

Step1: Identify the y - intercept (activation fee)

The y - intercept of a linear equation \(y = mx + b\) is the value of \(y\) when \(x = 0\). In the context of the problem, when \(x=0\) (months with the phone plan), the total spent \(y\) is the activation fee. From the graph, when \(x = 0\), \(y=\$25\).

Step2: Calculate the slope (monthly cost)

The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points \((x_1,y_1)=(0,25)\) and \((x_2,y_2)=(1,50)\) (we can also use other pairs of points). Then \(m=\frac{50 - 25}{1-0}=\frac{25}{1}=25\). The slope represents the rate of change of the total cost with respect to the number of months, which is the monthly cost.

Answer:

After an activation fee of \(\$25\), the plan will cost Martin \(\$25\) per month.