The equation $P=31+1.75w$models the relation between the amount of Tuyet's monthly water bill payment, P, in dollars, and the number of units of water, w, used.

(a) Find Tuyet's payment for a month when 0 units of water are used.

(b) Find Tuyet's payment for a month when 12 units of water are used.

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

(d) Graph the equation.

The given equation is$P=31+1.75w$.

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

$\begin{array}{rcl}P& =& 31+1.75\left(0\right)\\ & =& 31+0\\ & =& 31\end{array}$

• So, Tuyet's payment is $31 when 0 units of water are used.

• Substitute 12 for w in the given equation and solve for P.

$\begin{array}{rcl}P& =& 31+1.75\left(12\right)\\ & =& 31+21\\ & =& 52\end{array}$

• So, Tuyet's payment is $52 when 12 units of water are used.

• The given equation is of the form $y=mx+b$. So, the slope is $1.75$.
• Substitute 0 for w in the given equation and obtain the value of P.

$\begin{array}{rcl}P& =& 31+1.75\left(0\right)\\ & =& 31\end{array}$

• So, $\left(0,31\right)$is the P-intercept.

• Rewrite $m=1.75$in fractional form.

$\begin{array}{rcl}1.75& =& \frac{1.75}{1}\end{array}$

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

$\frac{1.75\left(100\right)}{1\left(100\right)}=\frac{175}{100}$

• From the point $\left(0,31\right)$, go up 175 units and then move 100 units to the right to obtain the second point.
• The second point will be $\left(100,206\right)$.
• Join the obtained points to plot the equation.