Question

Hello, What are the two inequalities that make up this graph

Answer 1

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.

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Let's plug in those points to the formula above and simplify into y = .

`\begin{gathered} y-4=(6-4)/(-2+4)(x+4)_{}_{} \\ y-4=(2)/(2)(x+4)_{} \\ y-4=1(x+4) \\ y=x+4+4 \\ y=x+8 \end{gathered}`

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.

`\begin{gathered} y-4=(1-4)/(-3+4)(x+4) \\ y-4=(-3)/(1)(x+4) \\ y-4=-3(x+4) \\ y-4=-3x-12 \\ y=-3x-12+4 \\ y=-3x-8 \end{gathered}`

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.