The required equation is ![y=\frac{1}{2} x+25](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B2%7D%20x%2B25)
<h3><u>Solution:</u></h3>
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}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B1%7D%7B2%7D)
Then from eqn 1,
![\begin{array}{l}{55=60\left(\frac{1}{2}\right)+c} \\\\ {c=55-30} \\\\ {c=25}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B55%3D60%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%2Bc%7D%20%5C%5C%5C%5C%20%7Bc%3D55-30%7D%20%5C%5C%5C%5C%20%7Bc%3D25%7D%5Cend%7Barray%7D)
Then our equation is modified as ![y=\frac{1}{2} x+25](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B2%7D%20x%2B25)