Question

Draw the graph of the equation 2x + 3y = 12. From the graph, find the coordinates of the point:

(i) whose y-coordinates is 3. (ii) whose x-coordinate is - 3.

Answer 1

$2x+3y=12\Rightarrow 2x=12-3yx=\frac{12-3y}{2}Ify=0,thenx=\frac{12-3\times 0}{2}=\frac{12-0}{2}=\frac{12}{2}=6Ify=4,thenx=\frac{12-3\times 4}{2}=\frac{12-12}{2}=\frac{0}{2}=0$

$\begin{array}{ccc}x& 6& 0\\ y& 0& 4\end{array}$

Plot the points (6, 0) and (0, 4) on the graph and join them to get the graph if the line.

(i) If y = 3, then draw perpendicular from y = 3 to the line, which get meets it at P then x-coordinate of p will be

$\therefore \text{coordinates of P are}(\frac{3}{2},3)$

(ii) If x = - 3, draw perpendicular from x = -3 to the line, which meets it Q. The y coordinates of Q will be y = 6

$\therefore$ co-ordinates of Q are (-3, 6)