Question

at the end of each month, tamera records the height of her plant on the line graph. during which month was her plants growth rate greatest? month 1 month 2 month 4 month 6

Explanation:

Step1: Recall growth - rate concept

Growth rate is change in height per unit time. On a line - graph of height vs time, it is the slope of the line segment between two points.

Step2: Calculate slopes for each month

For month 1: Let $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(1,3)$. Slope $m_1=\frac{y_2 - y_1}{x_2 - x_1}=\frac{3 - 0}{1 - 0}=3$.
For month 2: Let $(x_1,y_1)=(1,3)$ and $(x_2,y_2)=(2,5)$. Slope $m_2=\frac{y_2 - y_1}{x_2 - x_1}=\frac{5 - 3}{2 - 1}=2$.
For month 4: Let $(x_1,y_1)=(3,6)$ and $(x_2,y_2)=(4,7)$. Slope $m_4=\frac{y_2 - y_1}{x_2 - x_1}=\frac{7 - 6}{4 - 3}=1$.
For month 6: Let $(x_1,y_1)=(5,8)$ and $(x_2,y_2)=(6,9)$. Slope $m_6=\frac{y_2 - y_1}{x_2 - x_1}=\frac{9 - 8}{6 - 5}=1$.

Step3: Compare slopes

Since $m_1 = 3$, $m_2=2$, $m_4 = 1$, $m_6 = 1$, the largest slope is $m_1$.

Answer:

month 1