Question

adrennes cell phone bill last month was $31.80, and she talked for a total of 130 minutes. her bill the previous month was for $34.50, and she talked for 175 minutes. what linear function would represent this situation? a) $f(x)=0.6x + 45$ b) $f(x)=0.06x + 24$ c) $f(x)=0.06x + 45$ d) $f(x)=0.6x + 24$

Explanation:

Step1: Find the slope

The slope $m$ of a line given two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $x$ be the number of minutes and $y$ be the bill amount. We have $(x_1,y_1)=(130,31.80)$ and $(x_2,y_2)=(175,34.50)$. Then $m=\frac{34.50 - 31.80}{175 - 130}=\frac{2.7}{45}=0.06$.

Step2: Find the y - intercept

Use the point - slope form $y - y_1=m(x - x_1)$ with the point $(x_1,y_1)=(130,31.80)$ and $m = 0.06$. So $y-31.80=0.06(x - 130)$. Expand: $y-31.80=0.06x-7.8$. Add 31.80 to both sides: $y=0.06x+24$.

Answer:

B. $f(x)=0.06x + 24$