The equation graphed is written as
y ≤ 2x - 1
y > 1/2 x + 2
How to write the equations
The equation graphed is written in the slope intercept form s below
y = mx + c
where
m = slope
x = intercept
For the dashed line
The slope, m is calculated using the points on the graph (0, 2) and (4, 4)
m = (y₀ - y₁) / (x₀ - x₁)
m = (2 - 4) / (0 - 4)
m = (-2) / (-4)
m = 1/2
c = y intercept, from the graph is 2
c = 2
The equation of the line is y = 1/2 x + 2.
The inequality equation is y > 1/2 x + 2.
For the solid line
The slope, m is calculated using the points on the graph (0, -1) and (2, 3)
m = (y₀ - y₁) / (x₀ - x₁)
m = (-1 - 3) / (0 - 2)
m = (-4) / (-2)
m = 2
c = y intercept, from the graph is -1
c = -1
The equation of the line is y = 2 x - 1.
The inequality equation is y ≤ 2x - 1.