Question

answer the multiple - choice question. adrienne’s cell phone bill last month was $29.30 and she talked for a total of 130 minutes. her bill the previous month was for $34.25 and she talked for 175 minutes. what linear function would represent this situation? f(x)=53.61x f(x)=0.11x + 53.50 f(x)=0.11x + 15 f(x)=1.1x + 15

Explanation:

Step1: Find the slope

The slope $m$ of a linear - function $y = mx + b$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line. Let $x$ be the number of minutes and $y$ be the bill amount. We have $(x_1,y_1)=(130,29.30)$ and $(x_2,y_2)=(175,34.25)$. Then $m=\frac{34.25 - 29.30}{175 - 130}=\frac{4.95}{45}=0.11$.

Step2: Find the y - intercept

We use the point - slope form $y - y_1=m(x - x_1)$ and then convert it to the slope - intercept form $y=mx + b$. Using the point $(130,29.30)$ and $m = 0.11$, we have $y-29.30=0.11(x - 130)$. Expand the right - hand side: $y-29.30=0.11x-14.3$. Add 29.30 to both sides: $y=0.11x+(29.30 - 14.3)=0.11x + 15$.

Answer:

C. $f(x)=0.11x + 15$