Question

Use the graph of the line to answer the questions.

What is an equation of the line in point-slope form?
How can the point-slope form be written in function notation?

Answer 1

`y+1=(1)/(3)(x+2)` - point-slope form

`f(x)=(1)/(3)x-(1)/(3)` - function notation

Explanation:

The point-slope form of an equation of a line:

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

m - slope

The formula of a slope:

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

From the graph we have the points (-2, -1) and (1, 0).

Substitute:

`m=(0-(-1))/(1-(-2))=(1)/(3)`

`y-(-1)=(1)/(3)(x-(-2))`

`y+1=(1)/(3)(x+2)` - point-slope form

`y+1=(1)/(3)(x+2)` use the distributive property

`y+1=(1)/(3)x+(2)/(3)` subtract 1 = 3/3 from both sides

`y=(1)/(3)x-(1)/(3)`

Answer 2

Point slope form :
`y-0=(1)/(3)(x-1)`

Function notation :
`f(x)=(1)/(3)(x-1)`

Explanation:

If a line passes through two points
`(x_1,y_1)` and
`(x_2,y_2)`, then the point slope form of line is

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

Where, m is slope.

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

From the given graph it is clear that he line passes through the points (-2,-1) and (1,0). Slope of the line is

`m=(0-(-1))/(1-(-2))=(1)/(3)`

The point is (1,0) and slope is 1/3. So, the point slope form of the line is

`y-0=(1)/(3)(x-1)`

`y=(1)/(3)(x-1)`

Therefore the point slope form is
`y-0=(1)/(3)(x-1)`.

Replace y by f(x) to write the equation in function notation.

`f(x)=(1)/(3)(x-1)`

Therefore the function notation is
`f(x)=(1)/(3)(x-1)`.