Chapter SH, Problem 8.7MPS

(a)

To determine

To calculate: To graph the equation using slope and y-intercept

Answer to Problem 8.7MPS

Graph is plotted

Explanation of Solution

Given information: A gym charges a $\$59$ initiation fee plus $\$7.70$ per week that a person attends. The total cost $y$ can be given by $y=7.7x+59$ for $x$ 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:

Given that a gym charges a $\$59$ initiation fee plus $\$7.70$ per week that a person attends. The total cost $y$ can be given by $y=7.7x+59$ for $x$ weeks

On comparing the above equation with slope-intercept form of line

  $\begin{array}{l}c=7.7\\ y=59\end{array}$

Since y-intercept, $y=59$

This means point on graph is $\left(0,59\right)$

Also, slope $c=7.7$ , this means there is $7.7$ increase in y-coordinate with every $1$ unit increase in x-coordinate.

Thus, point on graph is $\left(1,66.7\right)$

Plotting the points on graph,

  

Conclusion:

Hence, the graph is plotted

(b)

To determine

To calculate: To state the slope and y-intercept using the graph of the equation

Answer to Problem 8.7MPS

The slope is $7.7$ and y-intercept is $59$

Explanation of Solution

Given information: A gym charges a $\$59$ initiation fee plus $\$7.70$ per week that a person attends. The total cost $y$ can be given by $y=7.7x+59$ for $x$ 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:

Given that a gym charges a $\$59$ initiation fee plus $\$7.70$ per week that a person attends. The total cost $y$ can be given by $y=7.7x+59$ for $x$ weeks

On comparing the above equation with slope-intercept form of line

  $\begin{array}{l}c=7.7\\ y=59\end{array}$

Conclusion:

Hence, slope is $7.7$ and y-intercept is $59$

(c)

To determine

To calculate: To describe what the slope and y-intercept represents

Answer to Problem 8.7MPS

Slope means that per week charge of person is $\$7.70$ , while y-intercept means that initial fee is $\$59$

Explanation of Solution

Given information: A gym charges a $\$59$ initiation fee plus $\$7.70$ per week that a person attends. The total cost $y$ can be given by $y=7.7x+59$ for $x$ 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:

Given that a gym charges a $\$59$ initiation fee plus $\$7.70$ per week that a person attends. The total cost $y$ can be given by $y=7.7x+59$ for $x$ weeks

On comparing the above equation with slope-intercept form of line

  $\begin{array}{l}c=7.7\\ y=59\end{array}$

Slope means that per week charge of person is $\$7.70$ , while y-intercept means that initial fee is $\$59$

Conclusion:

Hence, Slope means that per week charge of person is $\$7.70$ , while y-intercept means that initial fee is $\$59$