Chapter 8.7, Problem 26PPS

(a)

To determine

To calculate: To state slope and y-intercept of the graph of the equation and describe what they represent

Answer to Problem 26PPS

Slope is $\frac{3}{2}$ and y-intercept is $15$

Explanation of Solution

Given information: Sam has $15$ teaspoons of chopped nuts. She uses $1\frac{1}{2}$ teaspoons for each muffin. The total amount of nuts that she has left $y$ after $x$ muffins can be given by $y=-\frac{3}{2}x+15$ . Graph of equation is

  

Formula Used:

Slope intercept form of line is $y=mx+c$ , where

  $m=$ Slope of graph of equation

  $c=$ y-intercept of graph of equation

Calculation:

Equation is given as

  $y=-\frac{3}{2}x+15$

Comparing the above equation to slope intercept form of line $y=mx+c$ , slope and Y-intercept are

  $\begin{array}{l}m=-\frac{3}{2}\\ c=15\end{array}$

Slope represents the rate at which teaspoons of chopped nut is used

Y-intercept represents the amount of teaspoons of chopped nuts

(b)

To determine

To calculate: To name the x-intercept and describe what it represents

Answer to Problem 26PPS

x-intercept is $\left(10,0\right)$

Explanation of Solution

Given information: Sam has $15$ teaspoons of chopped nuts. She uses $1\frac{1}{2}$ teaspoons for each muffin. The total amount of nuts that she has left $y$ after $x$ muffins can be given by $y=-\frac{3}{2}x+15$ . Graph of equation is

  

Formula Used:

Slope intercept form of line is $y=mx+c$ , where

  $m=$ Slope of graph of equation

  $c=$ y-intercept of graph of equation

Calculation:

Equation is given as

  $y=-\frac{3}{2}x+15$

In order to find x-intercept, put $y=0$ in the above equation

  $\begin{array}{l}0=-\frac{3}{2}x+15\\ \frac{3}{2}x=15\\ x=15\times \frac{2}{3}\\ x=5\times 2\\ x=10\end{array}$

Hence, x-intercept is $\left(10,0\right)$

X-intercept represents number of muffins baked