Question

1 ptsQuestion 5Jane started jogging 5 miles from home, at a rate of 2 mph. Write the slope-intercept form of an equation for Jane's position relative to home.

Answer 1

Answer

$y=2x+5$

SOLUTION

Problem Statement

The question wants us to model the distance Jane is from her home given her initial starting point (5 miles from home) and her speed (2 mph)

Explanation

To solve the question, we simply need to model her jogging using the equation of a line.

The general equation of a line is given as:

$\begin{gathered} y=mx+c \\ \text{where,} \\ m=\text{slope}=\text{this represents Jane's speed} \\ c=y-\text{intercept}=\text{this represents her initial position from her home} \\ x=\text{time taken for Jane to move} \\ y=\text{Jane's final position after moving for time, x} \end{gathered}$

We have been told that her speed is 2 mph. Thus, m = 2. We have also been given her initial position from her house to be 5 miles.

Jane starts jogging 5 miles from her home, thus, her position relative to her home will continue to increase as she jogs on at 2 mph. Thus, c = 5 and NOT -5.

This means we can write the equation for her position is:

$\begin{gathered} m=2,c=5 \\ \therefore y=2x+5 \end{gathered}$

Final Answer

$y=2x+5$