Which inequality describes the graph above?
First, we find the equation of the boundary line using the two intercepts.The slope is
m = 4−00−5=45
The y-intercept is 4
The slope-intercept form of the equation is therefore
y = -45x+4
impliesy+45x=4
Multiply both sides by 54
implies54(y+45x)=4×54
implies54y+x=5
Multiply both sides by 4
⇒ 5y+4x=20
The inequality is therefore either 5y+4x≤20 or 5y+4x≥20.
Using the test point (0, 0) -The origin
⇒ 5(0) + 4(0) ≤ 20
⇒ 0 ≤ 20 (True)
∴ The inequality is 5y+4x≤20