Question

Draw the graph of each of the equations given below. Also, find the coordinates of the points where the graph cuts the coordinate axes:

$\left(i\right)6x-3y=12$ $\left(ii\right)-x+4y=8$ $\left(iii\right)2x+y=6$ $\left(iv\right)3x+2y+6=0$

Answer 1

$\left(i\right)6x-3y=12\Rightarrow 6x=12+3yx=\frac{12+3y}{6}=\frac{4+y}{2}$

$\begin{array}{ccc}x& 2& 0\\ y& 0& -4\end{array}$

$\left(ii\right)-x+4y=84y=8+xy=\frac{8+x}{4}$

$\begin{array}{ccc}x& 0& -4\\ y& 2& 1\end{array}$

$\left(iii\right)2x+y=6y=6-2x$

$\begin{array}{ccc}x& 0& 2\\ y& 6& 2\end{array}$

$\left(iv\right)3x+2y+6=0\Rightarrow 3x=-6-2y\Rightarrow x=\frac{-6-2y}{3}$

$\begin{array}{ccc}x& -2& 0\\ y& 0& -3\end{array}$

Now plot the points of each equation and join then we get four lines as shown on the graphs.

Equation (i) cuts the axes at (2, 0) and (0, -4)

Equation (ii) cuts the axes at (-8, 0) and (0, 2)

Equation (iii) cuts the axes at (3, 0), (0, 6) and

Equation (iv), cuts the axes at (-2, 0) and (0, -3)