[tex]\begin{gathered} slope_1=slope_2=2.25 \\ \end{gathered}[/tex]
Explanation
Step 1
when you have 2 coordinates ( A and B), the slope of the line that passes thought those point is given by
[tex]\text{slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
where
[tex]\begin{gathered} A=(x_1,y_1) \\ B=(x_2,y_2) \end{gathered}[/tex]
A and B are 2 known points of the line
Step 2
so, the slope represents the rate of change
i)the rate of change for 4-6 weeks
Let
A=(4 ,9)
B=(6,13.5)
replace
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ slope_1=\frac{13.5-9}{6-4}=\frac{4.5}{2}=2.25 \\ slope_1=2.25 \end{gathered}[/tex]
Step 3
ii)the rate of change for 6-9weeks
Let
A(6,13.5)
B(9,20.25)
replace,
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{20.25-13.5}{9-6}=\frac{6.75}{3}=2.25 \end{gathered}[/tex]
the slope represents the rate of change, it means for every case the plant is growing at a constant rate (2.25 inches per week)
I hope this helps you
