Answer: - (1/2)x + 2
Solution:
1) Table
x y
-2 3
0 2
4 0
6 -1
The first thing that you must probe is whether the relation is linear.
When the relation is linear the rate of change is constant.
The rate of change is Δy / Δx
2) Let's calculate that rate for all the points given:
x y
-2 3
0 2 ---> Δx = 0 -(-2) = 2, Δy = 2 - 3 = - 1 => Δy / Δx = - 1/2
4 0 ---> Δx = 4 - 0 =4, Δy = 0 - 2 = -2 => Δy / Δx = -2/4 = - 1/2
6 -1 ---> Δx = 6 - 4 = 2, Δy = - 1 - 0 = -1 => Δy / Δx = - 1/2
So, we have shown that the relation is linear.
3) Now, you can use the equation of the line: y = mx + b, where m is the slope (rate of change Δy / Δx) and b is the y-intercept.
We already found m = -1/2
The y-intercept is the value of y when x = 0, which you can get from the table; b = 2.
Therefore the equation is: y = (-1/2)x + 2.