Question

Which linear inequality is shown on the graph?

A)
x + 4y ≥ −4


B)
x + 4y ≤ −4


C)
4x + y ≥ −4


D)
4x + y ≤ −4

Answer 1

Make it a solid line for y≤ or y≥, and a dashed line for y< or y>
Shade above the line for a "greater than" (y> or y≥)
or below the line for a "less than" (y< or y≤).

So, the answer is A) x + 4y ≥ −4

x + 4y ≥ −4
4y ≥ -x - 4
y ≥ -x/4 - 1

Answer 2

Option A

Explanation:

The given graph is a solid line passing through two points ( -4, 0) and ( 0, -1 )

Let the equation of this line is y = mx+c

Where m = slope of the line =
`(y-y')/(x-x')`

=
`(0+1)/(-4-0)` = -
`((1)/(4))`

and y-intercept c = (-1)

therefore, equation will be y = (
`((-1)/(4))`)x + (-1)

y =
`((-x)/(4)-1`

4y = -x -4

x + 4y = -4

Since shaded region is above the line therefore inequality will be (x+4y ≥ -4)

Option A is the answer.