Question

Draw the graph of the line 4x + 3y = 24.

(i) Write the coordinates of the points where this line intersects the x - axis and the y - axis.

(ii) Use this graph to find the area of the triangle formed by the graph line and the coordinate axes.

Answer 1

For 4x + 3y = 24,

x	0	3	6
y	8	4	0
(x , y)	(0, 8)	(3, 4)	(6, 0)

Put, x = 0, we get y = 8

Put x = 3 we get y = 4 and

put x = 6 we get y = 0

(i) The coordinates of the points where this line intersects the x - axis and the y - axis are:

(0,8)(6,0)

(ii ) we have ∆ AOC,

With Base OC = 6 units, Height AO = 8 units,

We know that, A (∆ ABC) = ½ (Base) (Height)

∴ A(∆ AOC) = ½ (OC)(AO)

∴ A(∆ AOC) = ½ (6)(8)

∴ A(∆ AOC) = 3 × 8 = 24