Question

Maggie only wore sandals tracker on two of the days that she trained so from her fitness trackers she verified that on the third day she biked 20 miles and on the eighth day she biked 35 miles use these two data points to determine the equation of the line best of fit set for Maggie’s data

Answer 1

We know form our problem that the third day she biked 20 miles, so we have the point (3,20). We also know that on the eighth day she biked 35 miles, so our second point is (8,35).

To relate our two point we are going to use the slope formula: $m= \frac{x_{2}-x_{1}}{y_{2}-y_{1}}$
We can infer form our points that $x_{1}=3$, $y_{1}=20$,$x_{2}=8$, and $y_{2}=35$. so lets replace those values in our slope formula:
$m= \frac{35-20}{8-3}$
$m= \frac{15}{5}$
$m=3$

Now that we have the slope, we can use the point-slope formula determine the equation of the line that best fit the set for Maggie’s data.
Point-slope formula: $y-y_{1}=m(x-x_{1})$
$y-20=3(x-3)$
$y-20=3x-9$
$y=3x+11$

We can conclude that the equation of the line that  best fit the set for Maggie’s data is $y=3x+11$.