One of the great benefits of cartesian graphs (and the reason they were invented) is that they allow us to graphically demonstrate algebraic equation. For an equation (like 2y=3-x), every value of x can be related to a value of y. If we plot these values as (x,y) coordinates, the resulting graph is the graphical representation of our equation.

Let’s try doing drawing graphs for some simple equations:

Exercise

Let’s complete exercise 10 from page 58 of the core textbook:

All of the above graphs were lines. We can, of course, have graphs that are not straight lines. This will be influenced by the arithmetic operation (e.g. x², x³) used in the equation.

Let’s try plotting y = x²+1 on the graph above.

Exercise

Let’s complete exercise 11 from pages 59 and 60 of the core textbook:

The answers (where relevant) are below: