Graph of a function
We have the following equation:
y - 4 = 1/3 (x + 2)
We clear y in order to be more unterstandable:
y - 4 = 1/3 (x + 2)
y = 1/3 (x + 2) + 4
y = 1/3 x + 2/3 + 4
y = 1/3 x + 2/3 + 12/3
y = 1/3 x + 14/3
Step 1
In order to find the answer we are going to determine x value when y = 4:
y = 1/3 x + 14/3
4 = 1/3 x + 14/3
4 - 14/3 = 1/3 x
12 - 14 = x
-2 = x
Then, it passes through the point (-2 , 4), so we can discard options A and B (because it doesn't pass through (2, 4))
Step 2
We know a linear equation is given by:
y = mx + b, where m and b are numbers: m is the slope of the line and b the y-intercept.
In this case y = 1/3 x + 14/3, the slope is 1/3. We know m is given by
m = Δy/Δx
Since in this case
m = 1/3 = Δy/Δx
Then
Δx = 3 and Δy = 1
That means that if it changes 3 units on the x-axis, then it changes 1 unit on the y-axis