Question

Choose the linear inequality that describes the graph. The gray area represents the shaded region.

y > –5x – 3

y > –5x + 3

y > –3x + 5

y < –5x + 3

Answer 1

`y>-5x+3`

Explanation:

To find the linear inequality , Let pick two points from the graph

Lets pick (0,3) and (1,-2)

Lets find out slope using the points

`slope =(y_2-y_1)/(x_2-x_1)`

`slope =(-2-3)/(1-0)=-5`

Slope m= -5

y intercept b= 3

Equation of the line is y=mx+b

`y=-5x+3`

Now we look at the shaded part. we use test point (0,0)

(0,0) is not in the shaded region

`y=-5x+3`

`0=-5(0)+3`

0 >3 is false

`y>-5x+3`

Answer 2

y > –5x + 3

Explanation:

we know that

1) The solution of the inequality is the shaded area above the dashed line

so

The linear inequality could be

y > –5x – 3

y > –5x + 3

y > –3x + 5

2) The slope of the dashed line is negative ----> the three options have slope negative

3) The y-intercept of the dashed line is (0,3)

therefore

The linear inequality is

y > –5x + 3