Question

When Charlotte planted her tomato plant, it grew 3 inches in one week. After 5 weeks, the tomato plant was 23 inches tall. Assume the relationship is linear. Find and interpret the rate of change and the initial value.

Answer 1

the rate of change is 3 inches per week

The plant is 8 inches tall when it was planted

Explanation:

let x= the week number

y = height

(5,23) at 5 weeks it was 23 inches

m=3 inches per week (since it has linear growth, it must grow 3 inches per week every week)

the rate of change is 3 inches per week

to find the initial height we need to find the y intercept

to get that we start with point slope form

y-y1 = m(x-x1)

y-23 = 3 (x-5)

distribute

y-23 = 3x-15

add 23 to each side

y = 3x-15+23

y = 3x-8

the y intercept is 8 inches

The plant is 8 inches tall when it was planted