Answer:
y < x -2
y ≥ 2x + 5
Step-by-step explanation:
The dotted lines pass through (2, 0) and (-7, -9). Hence the slope of these line is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-9-0}{-7-2} =1[/tex]
The dotted line signifies a < or >. But signs the shaded portion is to the right, hence it is a <. The equation of the dotted line is given as:
[tex]y-y_1<m(x-x_1)\\\\y-0<1(x-2)\\\\y<x-2[/tex]
The straight line pass through (0, 5) and (-7, -9). Hence the slope of these line is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-9-5}{-7-0} =2[/tex]
The line signifies a ≥ or ≤. But signs the shaded portion is to the left, hence it is a ≥. The equation of the dotted line is given as:
[tex]y-y_1 \geq m(x-x_1)\\\\y-5\geq 2(x-0)\\\\y\geq 2x+5[/tex]
For the point (-10, -14)
y< x-2
-14 < -10 - 2
-14 < -12
y ≥ 2x + 5
-14 ≥ 2(-10) + 5
-14 ≥ -15
