Question

The table shows the height of a plant as it grows. what equation in point slope form gives the plants height at any time

time(months)/height(cm)
3/15
5/25
7/35
9/45​

Answer 1

`y - 15 = 5(x-3)`

Explanation:

Equation of a line:

The equation of a line, in point slope form, is given by:

`y - y_0 = m(x - x_0)`

In which the point is
`(x_0,y_0)` and m is the slope.

3/15

This means that
`x_0 = 3, y_0 = 15`

So

`y - 15 = m(x - 3)`

Finding the slope:

Suppose we have two points. The slope is given by the change in the output divided by the change in the input.

3/15

5/25

Change in the output: 25 - 15 = 10

Change in the input: 5 - 3 = 2

So

`m = (10)/(2) = 5`

The equation is:

`y - 15 = 5(x-3)`