Question

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

Answer 1

Inequality 1

Point 1 (0,5) Point 2 (-7 , -9)

slope = (-9 - 5) / (-7 - 0)

= -14/-7

= 2

y - 5 = 2(x - 0)

y - 5 = 2x

y = 2x + 5

y ≤ 2x + 5

Inequality 2

Point 1 (2, 0) Point 2 (-7, -9)

slope = (-9 - 0) / (-7 - 2)

= -9 / -9

= 1 (y - y1) = m(x - x1)

y - 0 = 1 (x - 2) m = 1

y = x - 2 x1 = 2 y1 = 0

y ≥ x - 2

System of inequalities y ≤ 2x + 5 and y ≥ x - 2

The point (-10, -14) is in the shaded area, so it is a solution of the system of inequalities.