Question

Draw the graph of each of the following linear equations in two variables:

$\left(i\right)x+y=4$ $\left(ii\right)x-y=2$ $\left(iii\right)-x+y=6$

$\left(iv\right)y=2x$ $\left(v\right)3x+5y=15$ (vi) $\frac{x}{2}-\frac{y}{3}=2$

(vii) $\frac{x-2}{3}=y-3$ $\left(viii\right)2y=-x+1$

Answer 1

$\left(i\right)x+y=4x=4-yify=0,thenx=4ify=4,thenx=0$

Now plot the points (4, 0) and (0, 4) on the graph and join them to get the graph of the given equation

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

$\left(ii\right)x-y=2x=2+yIfy=0,thenx=2andify=1,Thenx=2+1=3$

$\begin{array}{ccc}x& 2& 3\\ y& 0& 1\end{array}$

Now plot the points (2, 0) and (3, 1) on the graph and join them to get the graph of the equation.

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

$Ifx=0,theny=6+0=6Ifx=-1,theny=6-1=5$

$\begin{array}{ccc}x& 0& -1\\ y& 6& 5\end{array}$

Now plot the points (0, 6) and (-1, 5) on the graph and join them to get a graph of the line.

$\left(iv\right)y=2xIfx=0,theny=2\times 0=0Ifx=1,theny=2\times 1=2$

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

Now plot the points (0, 0) and (1, 2) on the graph and join them to get the graph of the line.

$\left(v\right)3x+5y=15\Rightarrow 3x=15-5y\Rightarrow x=\frac{15-5y}{3}Ify=0,thenx=\frac{15-5\times 0}{3}=\frac{15-0}{3}=\frac{15}{3}=5Ify=3,thenx=\frac{15-5\times 3}{3}=\frac{15-15}{3}=\frac{0}{3}=0$

$\begin{array}{ccc}x& 5& 0\\ y& 0& 3\end{array}$

Now plot the points (5, 0) and (0, 3) on the graph and join them to get the graph of the line.

$\left(vi\right)\frac{x}{2}-\frac{y}{3}=2\frac{3x-2y}{6}=2\Rightarrow 3x=12+2y\Rightarrow x=\frac{12+2y}{3}Ify=0,thenx=\frac{12+2\times 0}{3}=\frac{12+0}{3}=\frac{12}{3}=4Ify=-3,thenx=\frac{12+2\times (-3)}{3}=\frac{12-6}{3}=\frac{6}{3}=2$

$\begin{array}{ccc}x& 4& 2\\ y& 0& -3\end{array}$

Now plot the points (4, 0) and (2, -3) on the graph and join them to get the graph of the line.

$\left(vii\right)\frac{x-2}{3}=y-3\Rightarrow x-2=3y-9\Rightarrow x=3y-9+2=3y-7Ify=2,thenx=3\times 2-7=6-7=-1Ify=3,thenx=3\times 3-7=9-7=2$

$\begin{array}{ccc}x& -1& 2\\ y& 2& 3\end{array}$

Now plot the points (-1, 2) and (2, 3) on the graph and join them to get the graph of the line.

$\left(viii\right)2y=-x+1y=\frac{-x+1}{2}Ifx=1,theny=\frac{-1+1}{2}=\frac{0}{2}=0Ifx=-1,theny=\frac{-(-1)+1}{2}=\frac{1+1}{2}=\frac{2}{2}=1$

Now plot the points (1, 0) and (-1, 1) on the graph and join then to get the graph of the line.