Answer:
The general equation for a line (written in the slope-intersect form) is:
y = f(x) = a*x + b
Such that the line is already written in function notation.
Where a is the slope, and b is the y-intersect.
If a line passes through a point (x₁, y₁) and (x₂, y₂), the slope can be written as:
y = (y₂ - y₁)/(x₂ - x₁)
We know that the line in the graph passes through the points:
(-2, -1) and (2, 0)
Then the slope of the line will be:
a = (0 - (-1))/(2 - (-2)) = 1/4
Then the function for the line will be something like:
y = f(x) = (1/4)*x + b
Now we want to find the value of b.
Because we know that this function passes through the point (2, 0), this means that:
f(2) = 0 = (1/4)*2 + b
We can solve that for b:
0 = 2/4 + b
-2/4 = b
Then the function for the line is:
y = f(x) = (1/4)*x - 2/4
