Question

Draw the graphs of $x+3y+3=0$ and $3x-2y+6=0.$ Plot only three points per line and mark the intersection point.

Answer 1

$x+3y+3=0$

$⟹x=-3-3y$

Let, $y=0,$ then $x=-3-3\left(0\right)=-3$

Similarly, when $y=-1,x=0$ and when $y=1,x=-6$

$\therefore$ the coordinates are $(-3,0),(0,-1),(-6,1)$

Now,

$3x-2y+6=0$

$⟹2y=3x+6$

$⟹y=\frac{3x+6}{2}$

Let, $x=0$, $y=3$

Similarly, when $x=-2,y=0,$ and $x=2,y=6$

$\therefore$ the coordinates are $(0,3),(-2,0),(2,6)$

$\therefore$ the intersecting point is marked with the dark black dot