Question

You go to MetroPCS and can talk for 60 minutes with the plan for $55, and 90 minutes with a plan that cost $70. Write an equation in slope intercept form that represents the total cost Y of talking for X number of minutes with MetroPCS plan

Answer 1

The required equation is $y=\frac{1}{2} x+25$

Solution:

Given that , you go to MetroPCS and can talk for 60 minutes with the plan for $55, and 90 minutes with a plan that cost $70.  

We have to write an equation in slope intercept form that represents the total cost Y of talking for X number of minutes with MetroPCS plan.

We know that, slope intercept form of equation is y = mx + c

Where "m" is the slope of line and "c" is the y-intercept

Now, for 1st case, 60 minutes ⇒ $55

Substitute these values in our equation 55 = 60m + c ⇒ (1)

And for 2nd case 90 minutes ⇒ $70

By substituting those values in equation, 70 = 90m + c ⇒ (2)

Now, subtract (1) from (2)

90m + c = 70

60m + c = 55  

(-)---------------

30m + 0 = 15

$m = \frac{1}{2}$

Then from eqn 1,

$\begin{array}{l}{55=60\left(\frac{1}{2}\right)+c} \\\\ {c=55-30} \\\\ {c=25}\end{array}$

Then our equation is modified as $y=\frac{1}{2} x+25$