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

y < x -2

y ≥ 2x + 5

Explanation:

The dotted lines pass through (2, 0) and (-7, -9). Hence the slope of these line is:

`m=(y_2-y_1)/(x_2-x_1)`

`m=(-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<m(x-x_1)\\\\y-0<1(x-2)\\\\y<x-2`

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

`m=(y_2-y_1)/(x_2-x_1)`

`m=(-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