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:

For the equation of the dotted line,

Slope of the line =
`(y_2-y_1)/(x_2-x_1)`

Since the dotted lines passes through the points (-7, -9) and (2, 0)

Slope =
`(-9-0)/(-7-2)`

`m_1` = 1

Therefore, equation of the line passing through (2, 0) and slope = 1 will be,

y - y' = m₁(x - x')

y - 0 = 1(x - 2)

y = x - 2

Since, shaded area is below the dotted line,

y < x - 2 will be the inequality.

Slope of the solid line passing through (-7, -9) and (0, 5) is,

`m_2=(-9-5)/(-7-0)`

= 2

Therefore, equation of the line passing through (0, 5) and slope = 2 will be,

y - 5 = 2(x - 0)

y = 2x + 5

Since, the given line is a solid line and shaded area is above the line,

y ≥ 2x + 5 will be the inequality.

Since, (-10, -14) is lying in the common shaded area of both the inequalities, it will be the solution set of the graphed inequalities.