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

$$\begin{gathered} 4x+3y=24 \\ \Rightarrow 3y=-4x+24 \\ \Rightarrow y=\frac{-4x+24}{3} \end{gathered}$$
When x = 0, $y=\frac{-4\times 0+24}{3}=\frac{0+24}{3}=\frac{24}{3}=8$
When x = 3, $y=\frac{-4\times 3+24}{3}=\frac{-12+24}{3}=\frac{12}{3}=4$
When x = 6, $y=\frac{-4\times 6+24}{3}=\frac{-24+24}{3}=\frac{0}{3}=0$
Thus, the points on the line 4x + 3y = 24 are as given in the following table:

x	0	3	6
y	8	4	0

Plotting the points (0, 8), (3, 4) and (6, 0) and drawing a line passing through these points, we obtain the graph of of the line 4x + 3y = 24.



(i) It can be seen that the line 4x + 3y = 24 intersects the x-axis at (6, 0) and y-axis at (0, 8).

(ii) The triangle formed by the line and the coordinate axes is a right triangle right angled at the origin.

∴ Area of the triangle = $\frac{1}{2}\times 6\times 8$ = 24 square units