Chapter 5.1, Problem 6STP

Robi has run the first 4 miles of a race in 30 minutes. She reached the 6 mile point after 45 minutes. Without graphing, is the slope of the line that represents this situation positive, negative, zero, or undefined? What is the slope?

To determine

To calculate: slope of line

Answer to Problem 6STP

  $\frac{2}{15}$

Explanation of Solution

Given information: Distance travelled in 30 minutes is 4 miles and 6 miles in 45 minutes.

Formula used: Slope of a line joining points $\left(x_1,y_1\right),\left(x_2,y_2\right)$ is given by $\frac{y_2-y_1}{x_2-x_1}$ .

Calculation:

Slope is positive if one variable increases as the other variable increases.

Take the first variable as distance travelled and the second variable as time.

Consider the following table:

Time (minutes)	Distance travelled (miles)
30   $\left(x_1\right)$	4   $\left(y_1\right)$
45   $\left(x_2\right)$	6   $\left(y_2\right)$

Here, distance travelled (one variable) increases from 4 miles to 6 miles as time (other variable) increases from 30 minutes to 45 minutes.

So,

Slope is positive.

Take $\left(x_1,y_1\right)=\left(30,4\right),\left(x_2,y_2\right)=\left(45,6\right)$

Slope of a line joining points $\left(x_1,y_1\right),\left(x_2,y_2\right)$ is given by $\frac{y_2-y_1}{x_2-x_1}$ .

Therefore,

Slope $=\frac{6-4}{45-30}=\frac{2}{15}$