Question

draw the graph of each of the following linear equations 1)x/2-y/3=3​

Answer 1

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

Given linear equation is

$\rm \: \dfrac{x}{2} - \dfrac{y}{3} = 3$

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

$\rm \: \dfrac{0}{2} - \dfrac{y}{3} = 3$

$\rm \: 0 - \dfrac{y}{3} = 3$

$\rm \: - \dfrac{y}{3} = 3$

$\rm \: - y = 9$

$\rm\implies \:y \: = \: - \: 9$

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

$\rm \: \dfrac{x}{2} - \dfrac{0}{3} = 3$

$\rm \: \dfrac{x}{2} - 0 = 3$

$\rm \: \dfrac{x}{2} = 3$

$\rm\implies \:x = 6$

Substituting 'y = 3' in the given equation, we get

$\rm \: \dfrac{x}{2} - \dfrac{3}{3} = 3$

$\rm \: \dfrac{x}{2} - 1 = 3$

$\rm \: \dfrac{x}{2} = 3 + 1$

$\rm \: \dfrac{x}{2} = 4$

$\rm\implies \:x = 8$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 9 \\ \\ \sf 6 & \sf 0 \\ \\ \sf 8 & \sf 1 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , - 9), (6 , 0) & (8 , 3)

➢ See the attachment graph.