Here we start with y = x line and move the line vertically upwards. Or downwards.

So, the new line is parallel and each point on y=x goes up vertically by 1 as shown in the picture and thus the new line is y=x+1. Similarly, if you push y=x down by 1, you get another parallel line y=x-1

So, the new line is parallel and each point on y=x goes up vertically by 1 as shown in the picture and thus the new line is y=x+1. Similarly, if you push y=x down by 1, you get another parallel line y=x-1

**what if we change the line to y = – x and push it up and down by 1**

**You can do this with any Straight Line**
In the diagram we have taken the angle of the slope as 30 degrees. And the line now is y=mx with m=tan 30

And thus the line which will be 4 units up vertically, will be y=mx+4 and as shown, the line which is pushed down by 6 units will have an equation y=mx-6

**This understanding will give you an intuitive feel for the general equation of the straight line y=mx+c**