Question

On a graph sheet, draw the graph of x - y + 1 = 0 and 3x + 2y - 12 = 0 on the same graph. Determine the:

i) Coordinates of the points of intersection of the lines with the axes.

ii) Area of triangle bounded by the lines and X-axis.​

Answer 1

The graphs of x – y + 1 = 0 and 3x + 2y – 12 = 0 are as shown in the below figure.

The area bounded by these lines and y-axis is 15/2 sq.units.

Given equations are:

x – y + 1 = 0 and 3x + 2y – 12 = 0

x - y + 1 = 0

when x = 0, y = -1

when y = 0, x = 1

We have obtained 2 points (0, -1) and (1, 0)

3x + 2y – 12 = 0

when x = 0, y = 6

when y = 0, x = 4

We have obtained 2 points (0, 6) and (4, 0)

The coordinates of the vertices of the triangle formed by these lines and x-axis are:

(2, 3), (-1, 0) and (4, 0)

The area bounded by these lines and x-axis is:

= 1/2 [x1 ( y2 - y3 ) + x2 ( y3 - y1 ) + x3 ( y1 - y2 )]

= 1/2 [2 ( 0 - 0 ) + (-1) (0 - 3 ) + 4 ( 3 - 0 )]

= 1/2 [ 2 (0) - 1 (-3) + 4 (3) ]

= 1/2 [ 0 + 3 + 12 ]

= 1/2 [ 15 ]

= 15/2 sq. units.