Question

Write the linear inequality shown in the graph.The gray area represents the shaded region.

Answer 1

Answer is D
for these you need to look at first what is your y-intercept from this graph it is -4 so that cancels out a and c.
Now you look if the gray area is above or below the line in this case it is above the line so y needs to be greater than the line to be a true statement.

Answer 2

`y\geq 3x-4`

Explanation:

First we find the equation for the graph line y=mx+b

where m is the slope and b is the y intercept

LEts pick two points from the line

(0,-4) and (2,2)

y intercept is -4 , the value of b= -4

to find slope m we use formula

`m=(y_2-y_1)/(x_2-x_1) =(-4-2)/(0-2) =3`

m=3 and b= -4

EQuation of a line is
`y=3x-4`

Now we write the inequality, we use test point 0,0 that is in shaded region

LEts plug in 0 for x and 0 for y

`y=3x-4`

`0=0-4`

0=-4

0>=-4 is true

So we use >= symbol

`y\geq 3x-4`