Inequality that represents the graph
[tex]y>\:-\frac{3}{2}x-2[/tex]
Option A
Explanation :
Given the graph of a linear inequality
Lets frame the linear equation of the dotted line first
Slope intercept form of linear equation is y=mx+b
where m is the slope and b is the y intercept
In the graph y intercept is -2. So value of b=-2
Now find out slope m using any two point on the dotted line
Lets pick (0,-2) and (-2,1)
slope formula
[tex]\frac{y_2-y_2}{x_2-x_1}[/tex]
Substitute the values of two points and find out slope
[tex]slope =\frac{y_2-y_2}{x_2-x_1}=\frac{1+2}{-2-0}=-\frac{3}{2}[/tex]
Now replace the values in equation y=mx+b
[tex]y=-\frac{3}{2} x-2[/tex]
In the graph we have dotted line so we use < or >
Lets use test point (0,0) origin.
x=0 and y=0
[tex]y=-\frac{3}{2} x-2\\0=-\frac{3}{2} (0)-2\\0=-2\\0>-2\\[/tex]
So the inequality becomes
[tex]y>-\frac{3}{2} x-2[/tex]
Learn more : brainly.com/question/5529505
