Question

Which linear inequality is shown on the graph?

Answer 1

Answer:

Option A

Step-by-step 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 = $\frac{y-y'}{x-x'}$

              = $\frac{0+1}{-4-0}$ = -$(\frac{1}{4})$

and y-intercept c = (-1)

therefore, equation will be y = ($(\frac{-1}{4})$)x + (-1)

                                            y = $(\frac{-x}{4}-1$

                                           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.

Answer 2

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