Answer::
[tex]y\ge\frac{4}{3}x+4[/tex]Explanation:
The first step is to determine the equation of the boundary line in slope-intercept form.
Find the slope of the line using the points (0,4) and (-3,0).
[tex]\begin{gathered} \text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{0-4}{-3-0} \\ =\frac{-4}{-3} \\ m=\frac{4}{3} \end{gathered}[/tex]The line intersects the y-axis at (0,4).
• Thus, y-intercept, b=4
Substitute into the slope-intercept form: y=mx+b
[tex]y=\frac{4}{3}x+4[/tex]This is the equation of the boundary line.
Next, we place the inequality.
• The boundary line is ,an unbroken line,, the possible inequalities are: ≤ or ≥
,• Since the shaded region is ,above the boundary line,, the inequality sign is ≥ (greater than or equal to).
Thus, the slope-intercept inequality for the graph is:
[tex]y\ge\frac{4}{3}x+4[/tex]