To identify the inequality graphed you need to identify the equation of the line that limits the inequality:
To identify the equiation of the line you need to dinf the slope:
Use two points on the line: (0 , - 4) and (3,0)
Formula to find the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]m=\frac{0-(-4)}{3-0}=\frac{4}{3}[/tex]
The y - intercept (b) is the value of y when x=0 in this case the b is -4
You have the equation in slope-interpcept form:
[tex]\begin{gathered} y=mx+b \\ \\ y=\frac{4}{3}x-4 \end{gathered}[/tex]
Substract -4/3 x in btoh sides of the equation:
[tex]\begin{gathered} y-\frac{4}{3}x=\frac{4}{3}x-\frac{4}{3}x-4 \\ \\ y-\frac{4}{3}x=-4 \end{gathered}[/tex]
Multiply both sides of the equation by 3:
[tex]3y-4x=-12[/tex]
Multiply for -1 both sides of the equation:
Equation of the line:
[tex]4x-3y=12[/tex]As the shadow area is under the line the inequality is:[tex]4x-3y\leq12[/tex]
