Question

a study was conducted to determine if age was a factor in how many daily hours a dog sleeps. the average daily sleeping hours was recorded for 22 dogs on the scatter plot above. which linear equation below fits the best fit line on the scatter plot above?
a ( y = - \frac { 4 } { 9 } x + 11 )
b ( y = \frac { 4 } { 9 } x + 11 )
c ( y = - \frac { 15 } { 9 } x + 11 )
d ( y = \frac { 15 } { 9 } x + 11 )

Explanation:

Step1: Determine the slope sign

Since the line is decreasing (as age \(x\) increases, sleep hours \(y\) decreases), the slope \(m\) is negative. So we can eliminate options B and D (which have positive slopes).

Step2: Estimate the slope value

Take two points on the line (approximate). Let's assume \((x_1,y_1)=(0,11)\) (y - intercept) and another point \((x_2,y_2)=(9,7)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting the values: \(m=\frac{7 - 11}{9-0}=\frac{- 4}{9}\)

Answer:

A. \(y =-\frac{4}{9}x + 11\)