Question

video game
the equation for the line of best fit is $y = 30x + 7$. according to the equation, which of these statements is true?
oscars high score increased by about 30 points for every 7 days he played.
oscars high score increased by about 30 points for each day he played.

Explanation:

Step1: Recall the slope - intercept form

The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. In the given equation \(y = 30x+7\), \(x\) represents the number of days and \(y\) represents the high score.

Step2: Interpret the slope

The slope \(m = 30\). In the context of the problem, the slope represents the rate of change of \(y\) (high score) with respect to \(x\) (number of days). The formula for slope is \(m=\frac{\Delta y}{\Delta x}\). Here, for a change in \(x\) (number of days) by \(1\) unit (\(\Delta x = 1\)), the change in \(y\) (high score) is \(\Delta y=m\times\Delta x\). Substituting \(m = 30\) and \(\Delta x=1\), we get \(\Delta y = 30\).

Answer:

Oscar’s high score increased by about 30 points for each day he played.