Question

on saturday, liam noticed a sprout had emerged from his garden. each day since, he has been measuring its growth. there is a linear relationship between the time, in days, since liams first observation, and the height of the sprout, in centimeters.

Explanation:

Step1: Recall slope - rate of change formula

The rate of change of a linear relationship is the slope of the line. The formula for slope $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.

Step2: Select two points on the line

Let's take the points $(0,2)$ and $(10,9)$. Here $x_1 = 0,y_1=2,x_2 = 10,y_2 = 9$.

Step3: Calculate the slope

$m=\frac{9 - 2}{10-0}=\frac{7}{10}=0.7$.

Answer:

The height of the sprout increases by $0.7$ cm per day.