Question

Sketch the graph of the equation 3x + 5y = 15. Find the area of the figure formed by this line and the two axes.

Answer 1

The graph of the equation 3x + 5y = 15 is as follows:


The figure formed by the line and the two axes is a right angled $∆$AOB.

$$\begin{gathered} \mathrm{In}∆\mathrm{AOB},\angle \mathrm{AOB}=90°,\mathrm{AO}=3\mathrm{units}\mathrm{and}\mathrm{BO}=5\mathrm{units} \\ \mathrm{Now}, \\ \mathrm{ar}\left(∆\mathrm{AOB}\right)=\frac{1}{2}\times \mathrm{AO}\times \mathrm{BO} \\ =\frac{1}{2}\times 3\times 5 \\ =\frac{15}{2} \\ =7.5\mathrm{square}\mathrm{units} \end{gathered}$$