To determine the two inequalities, let's check it one by one.
A. First graph (the one leaning to the right).
Let's get 2 points on the graph.
For our first graph, we have two points and these are (-4, 4) and (-2, 6). Let's determine the equation using Two-Point Form Formula.
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Let's plug in those points to the formula above and simplify into y = .
[tex]\begin{gathered} y-4=\frac{6-4}{-2+4}(x+4)_{}_{} \\ y-4=\frac{2}{2}(x+4)_{} \\ y-4=1(x+4) \\ y=x+4+4 \\ y=x+8 \end{gathered}[/tex]
The equation of the line is y = x + 8 however, since there is a shade below the solid line, the inequality is y ≤ x + 8. This is our first inequality.
B. Second graph (line leaning to the left)
Let's get 2 points on the graph.
For second graph, we have two points and these are (-4, 4) and (-3, 1). Let's determine the equation using Two-Point Form Formula that we use above.
[tex]\begin{gathered} y-4=\frac{1-4}{-3+4}(x+4) \\ y-4=\frac{-3}{1}(x+4) \\ y-4=-3(x+4) \\ y-4=-3x-12 \\ y=-3x-12+4 \\ y=-3x-8 \end{gathered}[/tex]
The equation of the second line is y = -3x - 8 however, since there is a shade above the solid line, the inequality is y ≥ -3x - 8. This is our second inequality.
