Question

the equation for the line of best fit is y = 2x + 6.2. according to the equation, which of these statements is true? cameron increases his weekly running distance by about 2 miles each week. cameron increases his weekly running distance by about 6.2 miles each week.

Explanation:

Step1: Recall slope-intercept form

The equation of a line in slope - intercept form is \(y = mx + b\), where \(m\) is the slope (rate of change) and \(b\) is the y - intercept (initial value).

Step2: Identify \(m\) and \(b\) in \(y = 2x+6.2\)

In the equation \(y = 2x + 6.2\), the slope \(m = 2\) and the y - intercept \(b = 6.2\). The slope represents the rate of change of \(y\) with respect to \(x\). Here, \(x\) is the number of weeks and \(y\) is the weekly running distance. So the rate of change of the weekly running distance with respect to the number of weeks is 2 miles per week. This means that Cameron increases his weekly running distance by about 2 miles each week. The value \(6.2\) is the initial distance (when \(x = 0\), i.e., at week 0), not the rate of increase.

Answer:

Cameron increases his weekly running distance by about 2 miles each week.