Chapter 8.5, Problem 3GP

(a)

To determine

To calculate: To write an equation that relates cost and weight of the apples

Answer to Problem 3GP

Equation that relates cost and weight of the applesis $4x-5y=0$

Explanation of Solution

Given information: Graph showing the cost $y$ of $x$ pounds of apples at the local grocery store

  

Formula Used:

Equation of line passing through the points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is given as follows:

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

Calculation:

Graph showing the cost $y$ of $x$ pounds of apples at the local grocery store

  

From graph, two points on line are

  $\left(0.5,0.40\right)$

  $\left(1.25,1\right)$

Equation of line passing through the above points is

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

Substituting the value in above formula,

  $y-0.40=\frac{1-0.40}{1.25-0.5}\left(x-0.5\right)$

Solving the above equation,

  $\begin{array}{l}y-0.40=\frac{0.6}{0.75}\left(x-0.5\right)\\ y-0.40=\frac{60}{75}\left(x-0.5\right)\\ y-0.40=\frac{4}{5}\left(x-0.5\right)\\ 5\left(y-0.40\right)=4\left(x-0.5\right)\\ 5y-2=4x-2\\ 4x-5y=0\end{array}$

Conclusion:

Hence, Equation that relates cost and weight of the apples is $4x-5y=0$

(b)

To determine

To calculate: To find the cost of $5$ pounds of apples

Answer to Problem 3GP

The cost of $5$ pounds of apples is $\$5$

Explanation of Solution

Given information: Graph showing the cost $y$ of $x$ pounds of apples at the local grocery store

  

Formula Used:

Equation of line passing through the points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is given as follows:

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

Calculation: Equation that relates cost and weight of the apples is given as follows:

  $4x-5y=0$

To calculate the cost of $5$ pounds of apple, substitute $x=5$ in above equation

  $\begin{array}{l}4\left(5\right)-5y=0\\ 5y=4\left(5\right)\\ y=\frac{4\times 5}{5}\\ y=5\end{array}$

Conclusion:

Hence, the cost of $5$ pounds of apples is $\$5$