Question

Graph these equations:x–y=-1y=x–2

Answer 1

We want to graph the equations

`\begin{gathered} x-y=-1 \\ y=x-2 \end{gathered}`

To do, for the first equation

`\begin{gathered} x-y=-1 \\ \text{put y = 0 and find x, we have } \\ x-0=-1 \\ x=-1 \\ Next,\text{ we put x = 0 and find y, we have } \\ x-y=-1 \\ 0-y=-1 \\ -y=-1 \\ \text{cancelling out the minus signs } \\ y=1 \end{gathered}`

Hence for the first equation, x = - 1 and y = 1, so we place two dots at x = - 1 and y = 1, and draw a straight-line to join the points.

For the second equation

`\begin{gathered} y=x-2 \\ \text{first put y = 0 to find x, we have } \\ 0=x-2 \\ x=2 \\ \text{Next we put x = 0 to find y, we have } \\ y=x-2 \\ y=0-2 \\ y=-2 \end{gathered}`

Hence, we place dots or points at x = 2 and y = -2 and join the points with a straight-line. Our graph becomes