Question

Cherie works in retail and her weekly salary includes commission for the amount she sells. The equation $S=400+0.15c$models the relation between her weekly salary, S, in dollars and the amount of her sales, c, in dollars.

(a) Find Cherie's salary for a week when her sales were \(0.

(b) Find Cherie's salary for a week when her sales were \)3,600.

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

(d) Graph the equation.

Short answer

(a) The salary is $400 for sales $0.

(b) The salary is $940 for sales $3600.

(c) Slope is $0.15$and $\left(0,400\right)$is the S- intercept.

(d)

Step-by-step solution

Part (a). Step 1. Given information

The given equation is$S=400+0.15c$.

Part (a). Step 2. Substitute and simplify

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

$\begin{array}{rcl}S& =& 400+0.15\left(0\right)\\ & =& 400\end{array}$

• So, the salary is $400 for sales $0.

Part (b). Step 1. Substitute and simplify

• Substitute 3600 for c in the given equation and solve for S.

$\begin{array}{rcl}S& =& 400+0.15\left(3600\right)\\ & =& 400+540\\ & =& 940\end{array}$

• So, the salary is $940 for sales $3600.

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 $0.15$.
• Substitute 0 for c in the given equation and obtain the value of S.

$\begin{array}{rcl}S& =& 400+0.15\left(0\right)\\ & =& 400\end{array}$

• So, $\left(0,400\right)$is the S-intercept.

Part (d). Step 1. Simplify the slope

• Rewrite $m=0.15$in fractional form.

$0.15=\frac{0.15}{1}$

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

$\frac{0.15\left(100\right)}{1\left(100\right)}=\frac{15}{100}$

Part (d). Step 2. Graph

• From the point $\left(0,400\right)$, go up 15 units and then move 100 units to the right to obtain the second point.

• The second point will be $\left(100,415\right)$.
• Join the obtained points to plot the equation.