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

$$2 x+3 y=12\cdots(1)$$

To draw the graph ,we need at least two solutions of the equation

Put $$x=0$$ in $$(1)$$

$$2(0)+3 y=12$$

$$\implies 3 y=12$$

$$\implies y=4$$

So $$\left(0,4\right)$$ is a solution of the equation

Put $$y=0$$ in $$(1)$$

$$2 x+3(0)=12$$

$$\implies 2 x= 12$$

$$\implies x=6$$

So $$(6,0)$$ is a solution of the equation

With these two equations we can draw graph of $$2x+3y=12$$

from the graph

$$\text{(i)} $$ when $$y=3$$ then $$x=1.5$$

So, point is $$(1.5,3)$$

$$\text{(ii)} $$ when $$x=-3$$ then $$y=6$$

So, point is $$(-3,6)$$