Question

hockey games
the equation for the line of best fit is ( y = -\frac{1}{2}x + 6 ). according to the equation, which of these statements is true?
the team could expect to score about 6 goals in a game if they do not receive any penalties.
the team could expect to score about 1 additional goal for every 2 penalties they receive.

Explanation:

Step1: Analyze the y - intercept

The equation of the line is \(y =-\frac{1}{2}x + 6\). In the slope - intercept form \(y=mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept), when \(x = 0\) (no penalties, since \(x\) represents the number of penalties), we substitute \(x = 0\) into the equation: \(y=-\frac{1}{2}(0)+6=6\).

Step2: Analyze the slope

The slope \(m =-\frac{1}{2}\). The slope \(m=\frac{\Delta y}{\Delta x}\). A slope of \(-\frac{1}{2}\) means that for every increase of \(2\) in \(x\) (number of penalties), \(y\) (number of goals) decreases by \(1\). That is, the team scores \(1\) fewer goal for every \(2\) penalties.

Answer:

The team could expect to score about 6 goals in a game if they do not receive any penalties.