Chapter 8.8, Problem 4GP

(a)

To determine

To calculate: To write the linear equation that shows the cost $y$ for $x$ half −hour lessons

Answer to Problem 4GP

Linearequation that shows the cost $y$ for $x$ half −hour lessons is $y=22x+25$

Explanation of Solution

Given information: The cost of $7$ half-hour piano lessons is $\$179$ and the cost of $11$ half-hour lessons is $\$267$

Formula Used:

Equation of line passing through two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is

  $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

Calculation:

Given that cost of $7$ half-hour piano lessons is $\$179$ and the cost of $11$ half-hour lessons is $\$267$

This means $\left(7,179\right)$ and $\left(11,267\right)$ must satisfy the equation.

Using the two-point form equation of line, equation is given as

  $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

Substituting the values in above equation,

  $y-179=\frac{267-179}{11-7}\left(x-7\right)$

Solving the above equation,

  $\begin{array}{l}y-179=\frac{88}{4}\left(x-7\right)\\ y-179=22\left(x-7\right)\\ y-179=22x-154\\ y=22x-154+179\\ y=22x+25\end{array}$

Hence, equation is $y=22x+25$

(b)

To determine

To calculate: To find the cost of $3$ half-hour lesson

Answer to Problem 4GP

Cost of $3$ half-hour lesson is $\$91$

Explanation of Solution

Given information: Linearequation that shows the cost $y$ for $x$ half −hour lessons is $y=22x+25$

Calculation:

From part (a), Linearequation that shows the cost $y$ for $x$ half −hour lessons is $y=22x+25$

To find the cost of $3$ half hour lessons, substitute $x=3$ in the above equation

  $y=22\left(3\right)+25$

On solving the equation,

  $\begin{array}{l}y=66+25\\ y=91\end{array}$

Hence, cost is $\$91$