Question

(02.04 MC) Write the equation of the line that passes through the points (3, 6) and (4, 10) using function notation. f(x) = 4x − 6 f(x) = x + 4 y = x + 4 y = 4x − 6

Answer 1

f(x) = 4x − 6

Explanation:

Answer 2

The equation of line in function notation is:

`f(x)=4x-6`

Step-by-step explanation:

Given points:

(3,6) and (4,10)

To find the equation of the line in function notation.

Solution:

In order to find the equation of the line we will first find the slope of the line.

The slope of a line passing through points
`(x_1,y_1)` and
`(x_2,y_2)` the slope can be given as:

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

Plugging in the given points to find the slope of the line.

`m=(10-6)/(4-3)`

`m=(4)/(1)`

∴
`m=4`

Equation of line can be written in point slope form as:

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

where
`(x_1,y_1)` is a point on the line.

Using point (3,6)

`y-6=4(x-3)`

Using distribution:

`y-6=4x-12`

Adding 6 both sides.

`y-6+6=4x-12+6`

`y=4x-6` [Equation of line]

To write the equation in function notation, we will replace
`y` with
`f(x)`.

So, the equation of the line in function notation can be given as:

`f(x)=4x-6`