Question

7. Draw the graphs of the equations x - y + 1 = 0 and 3x + 2y - 12 =)
coordinates of the vertices of the triangle formed by these lines and
shade the triangular region.
of linear​

Answer 1

Appropriate Question :-

Draw the graphs of the equations x - y + 1 = 0 and 3x + 2y - 12 =0 and find the coordinates of the vertices of the triangle formed by these lines with x - axis and

shade the triangular region.

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

Consider the linear equation

$\sf \: x - y + 1 = 0$

$\sf \: \implies \: y = x + 1$

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 1 \\ \\ \sf 1 & \sf 2 \\ \\ \sf - 1 & \sf 0 \end{array}} \\ \end{gathered}$

Now, Consider other equation of line

$\sf \: 3x + 2y - 12 = 0$

$\sf \:2y = 12 - 3x$

$\sf \: \implies \: y = \dfrac{12 - 3x}{2}$

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 6 \\ \\ \sf 2 & \sf 3 \\ \\ \sf 4 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points.

➢ See the attachment graph.

From graph, we concluded that required triangle bounded by the lines with x - axis is ABC having coordinates

Coordinates of A (2, 3)

Coordinates of B (4, 0)

Coordinates of C (0, - 1)