Chapter 5.1, Problem 33E

(a)

To determine

To write and graph: linearequation that represents the given situation.

Answer to Problem 33E

Person’s linear equation is $y=5x$

Friend’s linear equation is $y=3x+3$

Explanation of Solution

Given:

The personwalks for 5 miles per hour.

Friend starts 3 miles from the trailhead and walks 3 miles per hour.

Calculation:

Let x represent the number of hours walked & y represent the distance covered.

For both equations, use the slope-intercept form:

  $y=mx+b$

Person’s speed corresponds to the slope, $\text{m}=5$

  $\text{b}=0$ Since you start on the trailhead

  $y=5x+0$

  $y=5x$

  

Friend's speed corresponds to the slope, $\text{m}=3\text{ \&}\text{}\text{b}=3$ since he started $3\text{mile}$ from the trailhead.

  $y=3x+3$

  

Conclusion:

Person’s linear equation is $y=5x$

Friend’s linear equation is $y=3x+3$