Question

carlos coaches a youth hockey team. this scatter plot shows the number of penalties his team received and the number of goals they scored in each of their games this year. it also shows the line of best fit. 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 1 additional goal for every 2 penalties they receive. the team could expect to score about 6 goals in a game if they do not receive any penalties.

Explanation:

Step1: Analyze the slope - intercept form

The equation of the line of best fit is $y =-\frac{1}{2}x + 6$, which is in the form $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. Here, $m =-\frac{1}{2}$ and $b = 6$.

Step2: Interpret the slope

The slope $m=-\frac{1}{2}$ means that for every 1 - unit increase in the number of penalties ($x$), the number of goals ($y$) decreases by $\frac{1}{2}$. In other words, for every 2 penalties, the number of goals decreases by 1.

Step3: Interpret the y - intercept

The y - intercept $b = 6$ means that when $x = 0$ (i.e., the team receives 0 penalties), $y=6$. So the team could expect to score about 6 goals in a game if they do not receive any penalties.

Answer:

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