Slope of a line
Step 1: selecting two points of the graph
We are going to select the points when x = 0 and x = 2.
Observing the graph we see that when x = 0, then y = 1 - (0,1)
when x = 2, then y = 2 - (2, 2)
Now we have two points:
(x₁, y₁) = (0, 1)
(x₂, y₂) = (2, 2)
Step 2: change of variables
We are going to find how much the variables change from point 1 to point 2
Change of x:
Δx = x₂ - x₁ = 2 - 0 = 2
Δx = 2
Change of y:
Δy = y₂ - y₁ = 2 - 1 = 1
Δy = 1
Step 3: slope
The slope, m, is the division of the two found changes:
m = Δy/Δx = 1/2
Answer: D. 1/2
