Question

PLEASE HELP ME!! D:

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

Point-slope form:

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

Slope-intercept form:

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

Explanation:

You have points on that line at (-2, -1) and (1, 0). To find your slope using those points, use the slope formula.

`(y2-y1)/(x2-x1) \\\\(0-(-1))/(1-(-2)) \\\\(0+1)/(1+2) \\\\(1)/(3)`

Now that we have your slope, you can use your slope and one of your points to write an equation in point-slope form.

`y-y1=m(x-x1)\\y-0=(1)/(3) (x-1)\\y=(1)/(3) x-(1)/(3)`

To put it in function notation, substitute y for f(x).

`f(x)-0=(1)/(3) (x-1)\\f(x)=(1)/(3) x-(1)/(3)`

Answer 2

First answer is y+1=(1/3) (x+2)

Second answer is f(x) =(1/3) x-(1/3)