Question

the equation for the line of best fit is ( y = 3x - 15 ). according to the equation, which of these statements is true? a dogs weight increases by about 3 pounds for every additional inch in height. a dogs weight increases by about 1 pound for every 3 additional inches in height.

Explanation:

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

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. In the given equation \(y = 3x-15\), \(m = 3\) and \(b=-15\).

Step2: Interpret the slope

The slope \(m=\frac{\Delta y}{\Delta x}\). In the context of the problem, \(y\) represents weight (in pounds) and \(x\) represents height (in inches). The slope \(m = 3=\frac{\Delta y}{\Delta x}\), which means that for every unit increase in \(x\) (i.e., for every additional inch in height), \(y\) (weight) increases by 3 units (3 pounds).

Answer:

A dog's weight increases by about 3 pounds for every additional inch in height.