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

We draw the graph of given linear equations as follows :

x – y + 1 = 0

⇒ y = x + 1

We put the different values of x in this equation, then we get different values of y and we prepare the table of x, y for equation x – y + 1 = 0

Table 1

and 3x + 2y – 12 = 0

⇒ 2y = 12 – 3x ⇒ y = 12−3x/2

∴ We put the different values of x in this equation then we get different values of y and we prepare the table of x, y for equation 3x + 2y – 12 = 0

Table 2

Now, we plot the points (2, 3), (4, 5) and (5, 6) on the graph paper and we draw a graph which passes through these points.

∴ We get a graph of linear equation x – y + 1 = 0.

Again, we plot the points (0, 6), (2, 3) and (4, 0) on the graph paper and we draw a graph, which passes through these points.

∴ We get a graph of linear equation

3x + 2y – 12 = 0.

We observe that the graphs of linear equations x – y + 1 = 0 and 3x + 2y – 12 = 0 intersect at point (2, 3). The graphs of linear equations meet x-axis at points B and C. So, the coordinates of ABC formed are A(2, 3), B(-1, 0) and C(4, 0).