Question

Nigel and Phyllis train for a marathon. The equation y = 1.25z + 4 represents that Nigel currently runs 4 miles per week and increases his total miles per week, y, by 1.25 for a numberof weeks. The graph represents Phyllis's running mileage.

Answer 1

From Phyllis's graph:

$\begin{gathered} (x1,y1)=(0,6) \\ (x2,y2)=(4,9) \\ m=\frac{y2-y1}{x2-x1}=\frac{9-6}{4-0}=\frac{3}{4} \\ \text{ Using the point slope equation:} \\ y-y1=m(x-x1) \\ y-6=\frac{3}{4}(x-0) \\ y=\frac{3}{4}x+6 \\ y=0.75x+6 \end{gathered}$

At the start of training, Phyllis runs more miles per week than Nigel because Phyllis runs 6 miles per week, while Nigel runs 4 miles per week