Which inequality is shown in this graph?

Question

asked Jun 8, 2019 84.4k views

2 Answers

CAustin · Answer 1 · 2019-06-12T16:42:56+0000

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

$y\leq -3x+3$