Question

3 a taxi driver records the time required to complete various trips and the distance for each trip.
the best - fit line is given by the equation ( y = 0.467x + 0.417 ), where ( y ) represents the distance in miles and ( x ) represents the time for the trip in minutes.
a. use the best - fit line to estimate the distance for a trip that takes 20 minutes.
show your reasoning.
b. use the best - fit line to estimate the time for a trip that is 6 miles long.
show your reasoning.

Explanation:

Step1: Substitute \(x = 20\) into the equation \(y = 0.467x+0.417\)

$$y=0.467\times20 + 0.417$$
Calculate \(0.467\times20=9.34\)
$$y = 9.34+0.417$$

Step2: Calculate the sum

$$y=9.757$$

Step3: For part b, substitute \(y = 6\) into the equation \(y = 0.467x+0.417\)

$$6=0.467x + 0.417$$
Subtract \(0.417\) from both sides:
$$6 - 0.417=0.467x$$
$$5.583 = 0.467x$$

Step4: Solve for \(x\)

$$x=\frac{5.583}{0.467}\approx12$$

Answer:

a. The estimated distance for a 20 - minute trip is \(9.757\) miles.
b. The estimated time for a 6 - mile trip is approximately \(12\) minutes.