Question

Draw the graph of the linear equation 3x

+ 4y = 6. At what points, the graph cutsthe x-axis and the y-axis?​

Answer 1

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

Consider the line 3x + 4y = 6

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

$\rm :\longmapsto\: 3 \times 0 + 4y = 6$

$\rm :\longmapsto\:0 + 4y = 6$

$\rm :\longmapsto\:4y = 6$

$\bf\implies \:y = 1.5$

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

$\rm :\longmapsto\:3x + 4 \times 0 = 6$

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

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

$\bf\implies \:x = 2$

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

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

$\rm :\longmapsto\:3x + 12 = 6$

$\rm :\longmapsto\:3x = 6 - 12$

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

$\bf\implies \:x = - 2$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 1.5 \\ \\ \sf 2 & \sf 0 \\ \\ \sf - 2 & \sf 3 \end{array}} \\ \end{gathered}$

➢ Now draw graph using the points (0 , 1.5), (2 , 0) & (-2 , 3)

So, from graph we concluded that

• Point of intersection with x axis = (2, 0)

• Point of intersection with y axis = (0, 1.5)

➢ See the attachment graph.