Question

Patel's weekly salary includes a base pay plus commission on his sales. The equation $S=750+0.09c$models the relation between his weekly salary, S, in dollars and the amount of his sales, c, in dollars.

(a) Find Patel's salary for a week when his sales were 0.

(b) Find Patel's salary for a week when his sales were 18,540.

(c) Interpret the slope and S-intercept of the equation.

(d) Graph the equation.

Short answer

(a) Salary was $750 when sales were 0.

(b) Salary was $$2418.6$ when sales were 18,540.

(c) Slope is $0.09$and S-intercept is $\left(0,750\right)$.

(d)

Step-by-step solution

Part (a). Step 1. Given information

The given equation is$S=750+0.09c$.

Part (a). Step 2. Substitute and simplify

• Substitute 0 for c in the given equation and solve for S.

$\begin{array}{rcl}S& =& 750+0.09\left(0\right)\\ & =& 750\end{array}$

• So, salary was $750 when sales were 0.

Part (b). Step 1. Substitute and simplify

• Substitute 18,540 for c in the given equation and solve for S.

$\begin{array}{rcl}S& =& 750+0.09\left(18,540\right)\\ & =& 750+1668.6\\ & =& 2418.6\end{array}$

• So, salary was $\$2418.6$when sales were 18,540.

Part (c). Step 1. Determine the slope and C-intercept.

• The given equation is of the form $y=mx+b$where c in the given equation denotes x and S denotes y. So, the slope is $0.09$.
• Substitute 0 for c in the given equation and obtain the value of S.

$\begin{array}{rcl}S& =& 750+0.09\left(0\right)\\ & =& 750\end{array}$

• So, $\left(0,750\right)$is the S-intercept.

Part (d). Step 1. Simplify the slope

• Rewrite $m=0.09$in fractional form.

$0.09=\frac{0.09}{1}$

• Multiply the numerator and denominator of the obtained fraction by 100 and simplify.

$\frac{0.09\left(100\right)}{1\left(100\right)}=\frac{9}{100}$

Part (d). Step 2. Graph

• From the point $\left(0,750\right)$, go up 9 units and then move 100 units to the right to obtain the second point.

• The second point will be $\left(100,759\right)$.
• Join the obtained points to plot the equation.