To identify the inequality of the given graph:
1. Identify the equation of the borderline in slope-intercept form (y=mx+b)
- Find the slope (m): Use two points in the line in the next formula:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ Points\colon(-3,-3)and(3,1) \\ \\ m=\frac{1-(-3)}{3-(-3)}=\frac{1+3}{3+3}=\frac{4}{6}=\frac{2}{3} \end{gathered}[/tex]- Identify the y-intercept (b): the value of y where the line cross the y-axis (when x is 0)
b= -1
Equation of the border line:
[tex]y=\frac{2}{3}x-1[/tex]2, Identifify the inequality sing:
-When the inequality is < or > the borderline is a dotted line
-When the inequality is ≥ or ≤ the border line is a full line
-When the inequality is < or ≤ the shaded area is under the borderline
-When the inequality is > or ≥ the shaded are is over the borderline
In this case you have a dotted borderline and a shaded area under the borderline, then, the inequality is:
[tex]y<\frac{2}{3}x-1[/tex]