Question

what is the graph given the inequality -2x - 3y<6

Answer 1

$\large\underline{\sf{Solution-}}$

Given inequality is

$\red{\rm :\longmapsto\: - 2x - 3y < 6}$

Let we first plot the graph for

$\rm :\longmapsto\: - 2x - 3y = 6$

Substituting 'x = 0' in the given equation, we get

$\rm :\longmapsto\: - 2(0)- 3y = 6$

$\rm :\longmapsto\: - 3y = 6$

$\rm :\longmapsto\: y = - \: 2$

Substituting 'y = 0' in the given equation, we get

$\rm :\longmapsto\: - 2x - 3(0) = 6$

$\rm :\longmapsto\: - 2x = 6$

$\rm :\longmapsto\:x = - \: 3$

Substituting 'y = 2' in the given equation, we get

$\rm :\longmapsto\: - 2x - 3(2) = 6$

$\rm :\longmapsto\: - 2x -6 = 6$

$\rm :\longmapsto\: - 2x = 6 + 6$

$\rm :\longmapsto\: - 2x = 12$

$\rm :\longmapsto\: x = - \: 6$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 2 \\ \\ \sf - 6 & \sf 2 \\ \\ \sf - 3 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , - 2), (- 6 , 2) & (- 3 , 0)

➢ See the attachment graph.

Now, in order to solve the inequality, we use Origin Test.

Let we substitute x = 0 and y = 0 in the given inequality. If it satisfy the given inequality, we shades towards ( 0, 0 ) otherwise shade away from ( 0, 0 ).

So,

On substituting x = 0 and y = 0 in

$\rm :\longmapsto\: - 2x - 3y < 6$

we get

$\rm :\longmapsto\: - 2(0) - 3(0) < 6$

$\rm :\longmapsto\: - 0 - 0 < 6$

$\rm :\longmapsto\:0 < 6$

$\bf\implies \:(0,0) \: satisfy \: the \: given \: inequality.$

$\red{\rm :\longmapsto\:Hence \: shades \: towards \: (0,0)}$