Question

the equation for the line of best fit is $y = 5x + 25$. according to the equation, which of these statements is true?
on average, there would be about 25 additional skiers for each $1^circ$f increase in the daily high temperature.
there would be about 25 skiers on a day with a high temperature of $0^circ$f.

Explanation:

Step1: Analyze the linear equation \(y = 5x+25\)

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 \(y = 5x+25\), the slope \(m = 5\) and the \(y\) - intercept \(b = 25\).
The slope \(m = 5\) means that for each \(1\) unit increase in \(x\) (high temperature), \(y\) (number of skiers) increases by \(5\).
The \(y\) - intercept \(b = 25\) is the value of \(y\) when \(x = 0\).

Step2: Evaluate the first statement

The first statement says "On average, there would be about 25 additional skiers for each \(1^{\circ}F\) increase in the daily high temperature".
Since the slope \(m = 5\), for each \(1^{\circ}F\) increase in temperature (\(x\)), the number of skiers (\(y\)) increases by \(5\), not \(25\). So this statement is false.

Step3: Evaluate the second statement

The second statement says "There would be about 25 skiers on a day with a high temperature of \(0^{\circ}F\)".
When \(x = 0\) (high temperature \(x = 0^{\circ}F\)), substitute \(x = 0\) into the equation \(y=5x + 25\).
We get \(y=5\times0+25=25\). So this statement is true.

Answer:

The second statement "There would be about 25 skiers on a day with a high temperature of \(0^{\circ}F\)" is true.