Chapter 8.7, Problem 4GP

(a)

To determine

To calculate: To graph the equation

Answer to Problem 4GP

Graph of equation of line is plotted.

Explanation of Solution

Given information: Jack has written $30$ pages of novel. He plans to write $12$ pages per week until he has completed his novel. The total number of pages written $y$ can be represented by $y=12x+30$ , where $x$ is number of weeks.

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

  $y=12x+30$

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

  $\begin{array}{l}m=12\\ c=30\end{array}$

Thus, y-intercept is at $\left(0,30\right)$ , which is the first point

Also, $m=12$ , this means that one will rise 12 (up) and run 1(to the right)

Thus, other point is $\left(1,42\right)$

On plotting the graph,

  

(b)

To determine

To calculate: To state the slope and y-intercept

Answer to Problem 4GP

Slope is $25$ and Y-intercept is $35$

Explanation of Solution

Given information: Jack has written $30$ pages of novel. He plans to write $12$ pages per week until he has completed his novel. The total number of pages written $y$ can be represented by $y=12x+30$ , where $x$ is number of weeks.

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

  $y=12x+30$

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

  $\begin{array}{l}m=12\\ c=30\end{array}$

Slope represents the number of pages written per week

Y-intercept represents initial number of pages written