Question

Keith applies a new brand of fertilizer to his grass.

He finds that the rate at which the grass grows can be modeled by a linear function
He observes that the rate of growth is 1 centimeter every 3 days.
After 18 days, he measures the height of the grass to be 8 centimeters
The initial height of the grass was centimeters tall.​

Answer 1

`\large\boxed{\large\boxed{2cm}}`

Step-by-step explanation:

A linear function can be expressed by its slope-intercept form:

`y=mx+b`

Where m is the slope and b is the y-intercept.

The slope is the rate of change of the dependent variabe, y, the height in this case, per unit of the independent variable, x, the number of days in this case:

`m=(rise)/(run)=(\Delta y)/(\Delta x)=(1cm)/(3days)`

Using the values y = 18 days and x = 8cm, you can find the y-intercept:

`8cm=(1cm)/(3days)* 18days+b\\ \\ \\ b=8cm-6cm=2cm`

The initial height of the was is the height when x = 0, i.e. the same y-intercept, b: 2cm.