Question

the equation for the line of best fit is y = 18.4x + 9.8. according to the equation, which of these statements is true?a student could expect to spend about 10 extra minutes raking leaves for each additional tree in the students yard.a student could expect to spend about 18 extra minutes raking leaves for each additional tree in the students yard.

Explanation:

Step1: Recall the slope - intercept form of a linear equation

The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. In the given equation \(y=18.4x + 9.8\), \(x\) represents the number of trees and \(y\) represents the time (in minutes) spent raking leaves.

Step2: Interpret the slope

The slope \(m = 18.4\). In the context of this problem, the slope represents the change in \(y\) (time) for a unit change in \(x\) (number of trees). Mathematically, if \(x_1\) and \(x_2\) are two values of \(x\) (\(x_2=x_1 + 1\)), then \(y_1=18.4x_1+9.8\) and \(y_2=18.4(x_1 + 1)+9.8=18.4x_1+18.4 + 9.8\). The difference \(y_2 - y_1=(18.4x_1+18.4 + 9.8)-(18.4x_1+9.8)=18.4\).

Answer:

A student could expect to spend about 18 extra minutes raking leaves for each additional tree in the student's yard.