Question

PLZ help What system of linear inequalities is shown in the graph?

Answer 1

In order find the Inequalities, First we need to Find the Equations of Both the Lines.

Equation of First line :

It is passing through the Points (0 , 2) and (4 , 0)

⇒ Slope = $\frac{2 - 0}{0 - 4} = \frac{-2}{4} = \frac{-1}{2}$

⇒ Equation of the First Line : $y - 2 = \frac{-1}{2}(x)$

⇒ Equation of the First Line : x + 2y = 4

Equation of Second Line :

It is passing through the Points (1.5 , 0) and (0 , -3)

⇒ Slope = $\frac{0 + 3}{1.5 - 0} = \frac{3}{1.5} = 2$

⇒ Equation of the Second Line : y + 3 = 2x

⇒ Equation of the Second Line : 2x - y = 3

As the Shaded Area of the First Line is away from the Origin :

⇒ x + 2y ≥ 4

As the Shaded Area of the Second Line is towards the Origin and it is a Dotted line :

⇒ 2x - y < 3

So, the System of Linear Inequalities are :

⇒ x + 2y ≥ 4

⇒ 2x - y < 3