Question

Write the equation of the line that passes through the points (3, 6) and (5, 18) using function notation.

Answer 1

`f(x) = 6x - 12`

EXPLANATION

The given line passes through the points (3, 6) and (5, 18).

The slope of this line given by:

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

We plug in the points to get,

`m = (18 - 6)/(5 - 3) = (12)/(2) = 6`

The equation is given by

`y-y_1=m(x-x_1)`

We plug in the point and the slope to get,

`y - 6 = 6(x - 3)`

`y - 6 = 6x - 18`

`y = 6x - 18 + 6`

`y = 6x - 12`

Using function notation, we have

`f(x) = 6x - 12`

Answer 2

`f(x) = 6x -12`

Explanation:

We must write the function of the line in the form
`f (x) = mx + b`

First calculate the slope m

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

`y_2 = 18\\y_1 =6\\x_2=5\\x_1=3`

`m= (18-6)/(5-3) = 6`

Then

`f(x) = 6x +b`

To have b replaced a point in the function

`f(3)=6 = 6(3) +b\\\\6-18= b\\\\b=-12`

Finally the function is

`f(x) = 6x -12`