Question

Write a system of inequalities to match the graph and prove that the coordinate point (-10,-14) is in the solution set ​

Answer 1

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:

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{-9-0}{-7-2} =1$

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:

$y-y_1$

The straight line pass through (0, 5) and (-7, -9). Hence the slope of these line is:

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{-9-5}{-7-0} =2$

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:

$y-y_1 \geq m(x-x_1)\\\\y-5\geq 2(x-0)\\\\y\geq 2x+5$

For the point (-10, -14)

y< x-2

-14 < -10 - 2

-14 < -12

y ≥ 2x + 5

-14 ≥ 2(-10) + 5

-14 ≥ -15