Question

the graph shows the height, h, in itches of a plant after d days. What equation can you use to represent the situation?

Answer 1

From the given graph, we can note a linear behavior. In order to find the line equation, we need 2 points. One point is (0,0) and the other point is (6,4)

The line equation in slope-intercept form is

`h=md+b`

Since the slope formula for 2 point is

`m=(h_2-h_1)/(d_2-d_1)`

with

`\begin{gathered} (d_1_{},h_1)=(0,0) \\ (d_2,h_2)=(6,4) \end{gathered}`

we have that

`\begin{gathered} m=(4-0)/(6-0) \\ \text{which gives } \\ m=(4)/(6)=(2)/(3) \end{gathered}`

Then, our line equation has the form

`h=(2)/(3)d+b`

and we can find the y-intercept b by replacing one of the 2 points, The "easy" point in this case is (0,0), which gives

`\begin{gathered} 0=(2)/(3)(0)+b \\ \text{then} \\ 0=0+b \\ or \\ b=0 \end{gathered}`

Therefore, the answer is

`h=(2)/(3)d`

which corresponds to the last option from top to bottom