Question

Lynn is tracking the progress of her plant's growth. The plant is already 8 centimeters high. The plant grows 1.5 centimeters per day. Which function shows this relationship?  y=8x+1.5y=1.5x+8y=9.5x

Answer 1

Given the information, we know that the plant is already 8 centimeters, therefore that would be our intercept with the y-axis (i.e. b = 8). Now, to find the slope, we have that on the first day the plant grows 1.5 centimeters, therefore for day 1, the plant is 9.5 centimeters high. With this observations we have the following:

`\begin{gathered} \text{Given (0,8) and (1,9.5)} \\ m=(y_2-y_1)/(x_2-x_1) \\ \Rightarrow m=(9.5-8)/(1-0)=1.5 \\ m=1.5 \end{gathered}`

Using the formula y=mx+b, we obtain the desired function:

`\begin{gathered} y=mx+b \\ \Rightarrow y=1.5x+8 \end{gathered}`

Therefore, the function that shows the relationship is y=1.5x+8