Question

The equation $P=28+2.54w$models the relation between the amount of R and y's monthly water bill payment, P, in dollars, and the number of units of water, w, used.

(a) Find the payment for a month when R and y used 0 units of water.

(b) Find the payment for a month when R and y used 15 units of water.

(c) Intercept the slope and P-intercept of the equation.

(d) Graph the equation.

Short answer

(a) Monthly payment is $28 for 0 units of water.

(b) Monthly payment is $$66.1$for 15 units of water.

(c) Slope is $2.54$and $\left(0,28\right)$is the P-intercept.

(d)

Step-by-step solution

Part (a). Step 1. Given information

The given equation is$P=28+2.54w$.

Part (a). Step 2. Substitute and simplify

• Substitute 0 for w in the given equation and solve for P.

$\begin{array}{rcl}P& =& 28+2.54\left(0\right)\\ & =& 28\end{array}$

• So, monthly payment is $28 when 0 units of water are used.

Part (b). Step 1. Substitute and simplify

• Substitute 15 for w in the given equation and solve for P.

$\begin{array}{rcl}P& =& 28+2.54\left(15\right)\\ & =& 28+38.1\\ & =& 66.1\end{array}$

• So, monthly payment is $$66.1$ when 15 units of water are used.

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

• The given equation is of the form $y=mx+b$. So, the slope is $2.54$.
• Substitute 0 for w in the given equation and obtain the value of P.

$\begin{array}{rcl}P& =& 28+2.54\left(0\right)\\ & =& 28\end{array}$

• So, $\left(0,28\right)$is the P-intercept.

Part (d). Step 1. Simplify the slope

• Rewrite $m=2.54$in fractional form.

$2.54=\frac{2.54}{1}$

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

$2.54\times \frac{100}{100}=\frac{254}{100}$

Part (d). Step 2. Graph

• From the point $\left(0,28\right)$, go up 254 units and then move 100 units to the right to obtain the second point.
• The second point will be $\left(100,282\right)$.
• Join the obtained points to plot the equation.