Question

draw the graph of the equation 2 X + 3 y = 6 find the coordinates of the point where the graph cut the y axis​

Answer 1

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

Given linear equation is

$\purple{\rm :\longmapsto\:2x + 3y = 6}$

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

$\rm :\longmapsto\:2 \times 0 + 3y = 6$

$\rm :\longmapsto\: 0 + 3y = 6$

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

$\bf\implies \:y = 2$

➢ Substituting 'y = 4' in the given equation, we get

$\rm :\longmapsto\:2x + 3 \times 4 = 6$

$\rm :\longmapsto\:2x + 12 = 6$

$\rm :\longmapsto\:2x = 6 - 12$

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

$\bf\implies \:x = - 3$

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

$\rm :\longmapsto\:2x + 3 \times 0 = 6$

$\rm :\longmapsto\:2x + 0 = 6$

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

$\bf\implies \:x = 3$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 2 \\ \\ \sf 3 & \sf 0 \\ \\ \sf - 3 & \sf 4 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , 2), (3 , 0) & (- 3 , 4)

➢ See the attachment graph.

So, from graph we concluded that the graph cut the y - axis at (0, 2).