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**Hint:**To draw a line you need two of its points, which you can connect. To find two points, you can plug any value for one variable, and solve for the other. For example: let’s choose $x=0$

The equation becomes $0-1=y$ and so $y=-1$

If your line goes through two distinct points of the equation, then your line is correct.

**Complete step by step solution:**

As we know that given equation is:

$x-1=y...(i)$

This is a line, since write equation as in the form of $y-x+1=0$

Which follows the pattern of the general line $ax+by+c=0$

To draw a line you need two of its points. Which you can connect.

To find two points, you can plug any value for one variable and solve for the other.

Put $x=0$ the equation become $0-1=y$

And so $y=-1$

Therefore, the point will be $\left( 0,-1 \right)$

$x=0$ and $y=-1$

Put $x=1$ in the equation no. $(i)$

$1-1=y$

And so $y=0$

Therefore the second point will be $\left( 1,0 \right)$

First point to plot the graph is $\left( 0,-1 \right)$and second point to plot the point graph is $\left( 1,0 \right)$ then connect these two points and make the line.

Hence, in this way you can graph $x-1=y$

**Additional Information:**

Graph a line using slope intercept form is:

The equation of a line in explicit from is:

$y=mx+q,$ where $'m'$ is the slope and $'q'$ is the $y$-intercept.

It is easier to show the procedure with some examples.

$y=2,$ this is line parallel to $x$-axis and it passes from the point $P\left( 0,2 \right)$

$y=x+1,$ this line is parallel to bisector of the $I$ and $II$ quadrants and it passes from the point $P\left( 0,1 \right)$

Graph $\left\{ x+1\left[ -10,10,-5,5 \right] \right\}$

$y=-\dfrac{1}{2}x-1$ we have to find the point $P\left( 0,-1 \right)$ From this point we have to ‘count’ $2$ units. To the left and then $2$ units to the up. So we can find the point $Q\left( -2,0 \right)$ then we have to join the two points found.

**Note:**

Write the given equation in the general pattern as $ax+by+c=0$ Remember that here you have to draw a line on a graph so you will require two points for draw a line. So, as require two points you have to assume $x=0$ and $x=1$

Do not forget to connect this point as you have to draw a line.

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