Q49. - Algebra 2

Question

For Exercises 49 and 50, use the following information.

Namid is examining the calling card portion of his phoning bill. A 4-minute call at the night rate cost \(2.65 and a 10-minute call cost \) 4.75.

Write a linear equation to model this situation.

Step-by-Step Solution

Answer

The required linear equation is $y=0.35x+1.25$.

Step 1 – State the concept

The linear equation satisfied by the points $\left(a,b\right)$ and $\left(c,d\right)$ is given as $\frac{y-b}{x-a}=\frac{d-b}{c-a}$.

Step 2 – List the given data

It is given that a 4-minute call at the night rate cost $2.65 and a 10-minute call at the night rate cost $4.75.

 Let $x$ denote the duration of call, in minutes and $y$ denote the cost of the call at night rate.

 This implies that the points, $\left(4,2.65\right)$ and $\left(10,4.75\right)$ satisfy the required linear equation.

 Then, $\left(a,b\right)=\left(4,2.65\right)$ and $\left(c,d\right)=\left(10,4.75\right)$.

Step 3 – Write the equation

Put $\left(a,b\right)=\left(4,2.65\right)$ and $\left(c,d\right)=\left(10,4.75\right)$ in $\frac{y-b}{x-a}=\frac{d-b}{c-a}$ to get,

 

$\frac{y-2.65}{x-4}=\frac{4.75-2.65}{10-4}$

 

$\frac{y-2.65}{x-4}=\frac{2.1}{6}$  (Simplify)

 

$\frac{y-2.65}{x-4}=0.35$  (Simplify)

 

$\frac{y-2.65}{x-4}\left(x-4\right)=0.35\left(x-4\right)$  (Multiply both sides by $x-4$)

 

$y-2.65=0.35x-1.4$   (Simplify)

 

$y-2.65+2.65=0.35x-1.4+2.65$  (Add $2.65$ to both sides)

 

$y=0.35x+1.25$   (Simplify)

 

So, the required linear equation is $y=0.35x+1.25$.