Question

Henry's potato vine is growing like crazy! When he planted it, it was 2 inches long. Two weeks later it was 5 inches long. At 6 weeks, it was 11 inches long.

Answer 1

`y = (3)/(2)x +2`

Explanation:

Required:

Write an equation to represent this situation

Let x represents the number of weeks and y represents the growth.

When he planted it:

`(x_1,y_1) = (0,2)`

Two weeks later:

`(x_2,y_2) = (2,5)`

At 6 weeks:

`(x_3,y_3) = (6,11)`

Start by calculating the slope (m)

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (5-2)/(2-0)`

`m = (3)/(2)`

Then calculate the equation using:

`y - y_3 = m(x - x_3)`

`y - 11 = (3)/(2)(x - 6)`

`y - 11 = (3)/(2)x - 9`

Solve for y

`y = (3)/(2)x - 9+11`

`y = (3)/(2)x +2`