Question

The table shows the height of a plant as it grows. What equation in point-slope form gives the plant’s height at any time?

Time (months): 4; Plant Height (in): 12
Time (months): 8; Plant Height (in): 15
Time (months): 12; Plant Height (in): 18
Time (months): 16; Plant Height (in): 21

what is the slope:__________
equation in slope intercept form:__________

Answer 1

Slope = 3/4

Equation in slope intercept form:
`y=(3)/(4)x+9`

Explanation:

Pick any two points from the table say (4,12) and (8,15).

Slope is given by formula:

`m=(y_2-y_1)/(x_2-x_1)=(15-12)/(8-4)=(3)/(4)`

Now plug the value of slope m=3/4 and any point say (4,12) into point slope formula:

`y-y_1=m\left(x-x_1\right)`

`y-12=(3)/(4)\left(x-4\right)`

`y-12=(3)/(4)x-3`

`y=(3)/(4)x-3+12`

`y=(3)/(4)x+9`

Hence final answer in slope intercept form is
`y=(3)/(4)x+9`