Chapter 4: Q. 336 (page 521)

The equation $P = 31 + 1.75 w$ 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.

Short Answer

Expert verified

The payment for a month when $0$ units water is used is $$ 31$ .
The payment for a month when $12$ units water is used is $$ 52$ .
The slope is $175$ and $P$ intercept is $31$ . Here, slope interprets how much the monthly water bill payment changes when the units of water used changes. And, the $P$ intercept equals to $31$ denotes that Tuyet's payment is $$ 31$ when $0$ units of water is used.

Step by step solution

Given information

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

Determine the intercept

To find payment for a month when $0$ units of water is used substitute $w = 0$ in the given equation.

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

To find payment for a month when $12$ units of water is used substitute $w = 12$ in the given equation.

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

Interpret the slope and intersect and then graph the equation

Rewrite the equation:

$P = 1.75 w + 31$

Comparing the equation with slope intercept form of line where $m$ is slope and $b$ is $y$ intercept of the line:

$y = m x + c$

On comparing, the conclusion comes out that $P = 1.75 w + 31$ is in slope intercept form of a line in $P w$ Plane, where $1.75$ is the slope of line and the $P$ intercept is $31$ .