Question

janelle and xavier are training for a marathon. the equation and graph each represent the runners time in minutes, y, as a function of their distance in miles, x. janelle: y = 12x what is janelles speed? find the rate of change. janelles speed = minutes per mile.

Explanation:

Step1: Recall the slope - intercept form of a linear equation

The equation of a line is \(y = mx + b\), where \(m\) is the slope (rate of change). For Janelle's equation \(y = 12x\), it is in the form \(y=mx\) (where \(b = 0\)).

Step2: Identify the rate of change

In the context of \(y\) (time in minutes) as a function of \(x\) (distance in miles), the coefficient of \(x\) in the equation \(y = 12x\) represents the rate of change. The rate of change formula for a linear function \(y=f(x)\) is \(\frac{\Delta y}{\Delta x}\). Here, when \(x\) (distance) changes by 1 mile (\(\Delta x=1\)), \(y\) (time) changes by \(12\) minutes (\(\Delta y = 12\)). So the rate of change \(m=\frac{\Delta y}{\Delta x}=\frac{12}{1}=12\).

Answer:

12