# 8: y=mx+a; y=mx-a

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

what if we change the line to y = – x and push it up and down by 1
 As you can see once again, we can very easily conceive pushing up and down y=-x and we get two parallel lines y=-x+1 when we push up and y=-x-1 when we push y=-x down by 1

 Here we show that if we draw a vertical line from x=-5, as shown, or any point on the x axis, this vertical line cuts these three lines at distances of 1 each from each other which again proves that these three lines are parallel and at a distance of 1 vertically from each other.

﻿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