Question

agility course participants
the equation for the line of best fit is ( y = -\frac{6}{5}x + 38 ). according to the equation, which of these statements is true?
a dog that just started training would likely have a race time of about 38 seconds.
a dog that has been training for 10 months would likely have a race time of about 50 seconds.

Explanation:

Step1: Analyze the equation \(y =-\frac{6}{5}x + 38\)

The general form of a linear equation is \(y=mx + b\), where \(m\) is the slope and \(b\) is the \(y -\)intercept. In the equation \(y =-\frac{6}{5}x + 38\), when \(x = 0\) (a dog that just started training, \(x\) represents months of training), we substitute \(x = 0\) into the equation.

Step2: Substitute \(x = 0\) into the equation

When \(x = 0\), \(y=-\frac{6}{5}(0)+38\).
Since \(-\frac{6}{5}(0)=0\), then \(y = 38\).

Step3: Analyze the second statement

For the second statement, when \(x = 10\), we substitute \(x = 10\) into the equation \(y=-\frac{6}{5}x + 38\).
\(y=-\frac{6}{5}\times10+38\).
First, calculate \(-\frac{6}{5}\times10=- 12\).
Then \(y=-12 + 38=26
eq50\).

Answer:

A. A dog that just started training would likely have a race time of about 38 seconds.