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

$m=\frac{y2-y1}{x2-x1}$

we have

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

Substitute the values

$m=\frac{-3-3}{2-0}$

$m=\frac{-6}{2}$

$m=-3$

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

$y\leq -3x+3$