We are given : For 500 minutes she pays $35 total and for 1500 minutes used she pays $55 total.
So, we can put the given information in form of two coordinates :
( Number of minutes, Total amount).
(500, 35) and (1500, 55).
First we need to find the slope between those two coordinates.
[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(500,\:35\right),\:\left(x_2,\:y_2\right)=\left(1500,\:55\right)[/tex]
[tex]m=\frac{55-35}{1500-500}[/tex]
[tex]m=\frac{1}{50}[/tex]
Now applying slope-intercept form y=mx+b, where m is the slope and b is y-intercept.
y-intercept represents monthly fixed charge.
Plugging (x,y) = (500, 35) and slope m= 1/50 in slope-intercept form y=mx+b.
35 = 1/50 (500) +b
35 = 10 + b.
Subtracting 10 from both sides, we get
35-10 = 10-10 + b
b = 25.
Therefore, her monthly fixed charge is $25.
