Question

license plate game
the equation for the line of best fit is ( y=\frac{3}{4}x + 1 ). according to the equation, which of these statements is true?
the family wrote down about 3 more states with every 4 additional hours of driving.
the family wrote down about 4 more states with every 3 additional hours of driving.

Explanation:

Step1: Analyze the slope of the line of best fit

The equation of the line is \(y=\frac{3}{4}x + 1\). In the slope - intercept form \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept), the slope \(m=\frac{3}{4}\). The slope represents the rate of change of \(y\) with respect to \(x\). Here, \(y\) is the number of states and \(x\) is the number of hours. The slope \(m=\frac{\Delta y}{\Delta x}\). If \(\Delta x = 4\) (change in hours), then \(\Delta y=m\times\Delta x\). Substituting \(m = \frac{3}{4}\) and \(\Delta x=4\), we get \(\Delta y=\frac{3}{4}\times4=3\).

Step2: Interpret the slope value

The slope \(\frac{3}{4}\) means that for every increase of \(4\) units in \(x\) (hours of driving), \(y\) (number of states) increases by \(3\) units.

Answer:

The family wrote down about 3 more states with every 4 additional hours of driving.