Question

Which inequality is shown in this graph?

Answer 1

It’s the inequality in letter C

Answer 2

Step 1

Find the equation of the line

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

we have

`A(0,3)\ B(2,-3)`

Substitute the values

`m=(-3-3)/(2-0)`

`m=(-6)/(2)`

`m=-3`

The equation of the line in slope-intercept form is equal to

`y=mx+b`

where

m is the slope

b is the y-intercept

we have

`m=-3`

`b=3` ------> see the graph

substitute

`y=-3x+3`

Step 2

Find the equation of the inequality

we know that

The solution of the inequality is the shaded area below the solid red line

so

the inequality is

`y\leq -3x+3`

therefore

the answer is the option C

`y\leq -3x+3`