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Which inequality describes the graph above?

...
Which inequality describes the graph above?

Which inequality describes the graph above?

A.

4y+5x20

B.

5y+4x20

C.

4y+5x20

D.

5y+4x20

Correct answer is B

First, we find the equation of the boundary line using the two intercepts.The slope is

m = 4005=45

The y-intercept is 4

The slope-intercept form of the equation is therefore

y = -45x+4

y+45x=4

Multiply both sides by 54

54(y+45x)=4×54

54y+x=5

Multiply both sides by 4

5y+4x=20

The inequality is therefore either 5y+4x20 or 5y+4x20.

Using the test point (0, 0) -The origin

⇒ 5(0) + 4(0) ≤ 20

⇒ 0 ≤ 20 (True)

∴ The inequality is 5y+4x20