The given graph is an illustration of a piece wise linear equation.
See attachment for the graph and Jamie's work
From the graph, we have:
[tex]x \to[/tex] Time (minutes)
[tex]y \to[/tex] Distance (miles)
(a) When the runner begins the race
From the graph, we have:
[tex]x \to [0,12][/tex]
[tex]y \to [0,1][/tex]
This means that the runner runs a distance of 1 mile in 12 minutes
So; Jamie's description here is wrong because he misrepresented the axes.
The equation of this part of the is calculated as follows:
Start by calculating the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{1-0}{12-0}[/tex]
[tex]m = \frac{1}{12}[/tex]
The equation is then calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
[tex]y = \frac{1}{12}(x - 0) + 0[/tex]
[tex]y = \frac{1}{12}x[/tex]
(b) When his partner takes over
From the graph, we have:
[tex]x \to (12,20][/tex]
[tex]y \to (1,2][/tex]
This means that his partner runs a distance of 1 mile in 8 minutes
So; Jamie's description here is also wrong because he misrepresented the axes, again.
The equation of this part of the is calculated as follows:
Start by calculating the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{2-1}{20-12}[/tex]
[tex]m = \frac{1}{8}[/tex]
The equation is then calculated using:
[tex]y = m(x- x_1) + y_1[/tex]
[tex]y = \frac{1}{8}(x - 12) + 1[/tex]
[tex]y = \frac{1}{8}x - 1.5 + 1[/tex]
[tex]y = \frac{1}{8}x -0.5[/tex]
[tex]y = \frac{1}{8}x -\frac 12[/tex]
Hence, the piece wise function can be represented as:
[tex]y = \left \{ {{\frac 1{12}x. \ 0 \le x \le 12} \atop {\frac 18x + \frac 12, \ 12 < x \le 20}} \right.[/tex]
Read more about piece wise equations at:
https://brainly.com/question/14590682
