Question

<

←+
-6
6
4
U ←
2
-4
-6-
2
6
→x
Write an equation that represents the line.
Use exact numbers.

Answer 1

To find the equation in slope-intercept form, y = mx + b, we need to first find the slope using

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

In this case we have the two points (1,2) and (4,4), so our calculation looks like:

`m=(4-2)/(4-1) = (2)/(3)`
Notice this is the same "rise over run" that we can count out on the graph. If we start at (1,2) and go "up 2 units, right 3 units", then we end up at the point (4,4).

Now we need to find b. We have
`y = (2)/(3)x+b`, so we need to substitute in one of the points to find b. Let's use (1,2):

`2 = (2)/(3)\cdot 1+b`

`2 = (2)/(3)+b`

`2 - (2)/(3) =b`

`(4)/(3) =b`

This gives us our equation:
`y = (2)/(3)x+(4)/(3)`