(Maths GCSE) When equations are multiplied/divided or added/subtracted by a number, the graph of the equation changes. How do you draw the new graph?

The 2 main rules are:1. If the right hand side of the equation is multiplied/divided by a number, the gradient of the line increases or decreases.2. If a number is added to/subtracted from the right hand side of the equation, the line moves up or down.Let's use a straight line as an example: y=x is a normal straight line. Using rule 1: if the right hand side (RHS) of the equation is multiplied by 'a' (y=ax), then the gradient of the line increases by a. In other words, the gradient gets steeper. Similarly, if RHS is divided by a (y=x/a), the gradient decreases by a. So the gradient is less steep. Using rule 2: if a is added to RHS (y=x+a), then the line moves up 'a' spaces (rule 2). Similarly, if a is subtracted from RHS (y=x-a), the line moves down 'a' spaces.Another rule sometimes comes into play if the right hand side of the equation is more complicated than just 'x'. We've been talking about adding to/subtracting from the whole right hand side of an equation. But sometimes it can be useful to just add to/subtract from x. For example: let's say the original equation is y=5x. If 'a' is added to the whole function of x (y=5x+a), then the line moves up 'a' spaces. However, if a is only added to x ( y=5(x+a) ), then the line moves LEFT 'a' spaces. Similarly, if a is subtracted from x ( y=5(x-a) ), the line moves RIGHT 'a' spaces. So this gives us a 3rd rule:3. If a number is added to/subtracted from x, the line moves left or right.It can be a little tricky to learn these rules without seeing them so I've made a document with a summary of the rules and lots of examples. I'll email it to you so you can keep it for revision. If you have questions, write them down so we can discuss them in our next lesson.NOTE: for some reason the drop down menu would only let me choose Psychology University, however this is a GCSE level maths question.