Solution:
Given the scatter plot below:
A) To determine the equation of the line, we have
This implies that the line passes through the points (3, 10) and ((7, 7).
Thus, we have the equation to be evaluated as
[tex]\begin{gathered} y-10=(\frac{7-10}{7-3})(x-3) \\ \Rightarrow y-10=-\frac{3}{4}(x-3) \\ thus,\text{ } \\ y=-\frac{3}{4}(x-3)+10 \\ open\text{ parentheses,} \\ y=-\frac{3}{4}x+\frac{9}{4}+10 \\ \Rightarrow y=-\frac{3}{4}x+\frac{49}{4} \end{gathered}[/tex]
Thus, the equation of the line, in slope-intercept form, is
[tex]\begin{equation*} y=-\frac{3}{4}x+\frac{49}{4} \end{equation*}[/tex]
B) Based on the linear model, the number of hours Jerry worked on the day of the picnic, day 0, is
[tex]\begin{gathered} y=-\frac{3}{4}x+\frac{49}{4} \\ where \\ x=0, \\ y=-\frac{3}{4}(0)+\frac{49}{4} \\ \Rightarrow y=12.25\text{ hours} \end{gathered}[/tex]
Thus, Jerry worked 12.25 hours.
From the linear model, Jerry's setup time decreases by
[tex]0.75[/tex]
