Question

Draw the graphs of the equations \(x – y + 1 = 0 \)and \(3x + 2y – 12 = 0\). Determine the coordinates of the vertices of the triangle formed by these lines and the \(X\)-axis, and shade the triangular region.

Answer 1

The equation \(x − y + 1 = 0\), which can be rewritten as \(x = y − 1\), is represented by the following table of values:

\(x\)	\(0\)	\(1\)	\(2\)
\(y\)	\(1\)	\(2\)	\(3\)

The equation \(3x + 2y − 12 = 0\), which can be rewritten as \(x= 12-\dfrac{2y}{3}\), is represented by the following table of values:

x	\(4\)	\(2\)	\(0\)
y	\(0\)	\(3\)	\(6\)

The graphic representation is as follows.

The figure shows that the lines intersect at the point (2, 3). The lines also intersect the X-axis at (−1, 0) and (4, 0).

Therefore, the vertices of the triangle formed are (2, 3), (−1, 0), and (4, 0).