Chapter 1, Problem 2CT

To determine

To write: An equation of the line according to the given graph and then to interpret slope and $y-\mathrm{int}ercept$ .

Answer to Problem 2CT

Equation is $y=-\frac{1}{2}x+50$ , slope signifies that as the discount increases by $1\%$ price decreases by $\$0.5$ , $y-\mathrm{int}ercept$ means that when no discount is applied, then price of shoes is $\$50$ .

Explanation of Solution

Given Information: A plotted graph is given.

Calculation:

Slope intercept form: $y=mx+b$

where $m=\frac{y_2-y_1}{x_2-x_1}$

  $\begin{array}{l}m=\frac{40-50}{20-0}\\ \\ =\frac{-10}{20}\\ \\ =-\frac{1}{2}\end{array}$

As can be observed in graph, when $x=0,y=50$ .

  $\Rightarrow y-\mathrm{int}ercept=50$

Substituting the values derived so far in slope-intercept form,

  $y=-\frac{1}{2}x+50$

Interpretation:

Slope implies that as the discount increases by $1\%$ price decreases by $\$0.5$ , Values of $y-\mathrm{int}ercept$ means that when no discount is applied, then price of shoes is $\$50$ .

Thus, equation is $y=-\frac{1}{2}x+50$ , slope signifies that as the discount increases by $1\%$ price decreases by $\$0.5$ , $y-\mathrm{int}ercept$ means that when no discount is applied price is $\$50$ .