Chapter 8, Problem 13PT

To determine

To write: an equation in slope-intercept and explain the slope of the line

Answer to Problem 13PT

The equation of the line is: $y=30x+150$

The slope of 30 represents the ascending at 30 lb per week.

Explanation of Solution

Given:

  

Calculation:

Consider two points: $\left(0,150\right)$ and $\left(3,240\right)$ from the graph.

Consider that recycling cans is denoted by y and number of weeks required stands for x

The general form of equation of line in slope intercept form is: $y=mx+b$

Here, m represents slope and b stands for y intercept.

Step 1: Find slope of the line ( m )by using formula of two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$

  $m=\frac{y_2-y_1}{x_2-x_1}$

Consider that $\left(x_1,y_1\right)=\left(0,150\right)$ and $\left(x_2,y_2\right)=\left(3,240\right)$

Put the value in slope formula:

  $\begin{array}{c}m=\frac{240-150}{3-0}\\ =\frac{90}{3}\\ =30\end{array}$

Step 2: Put the value of $b=150$ and $m=30$ in formula.

  $y=30x+150$

The equation of the line by using slope intercept form is: $y=30x+150$

And, slope of 30 represents the ascending at 30 lb per week.

Conclusion:

Therefore, equation of the line is: $y=30x+150$ and the slope of 30 represents the ascending at 30 lb per week.