A Demonstration

Take the graph of 𝑦 = 𝑥² that looks something like this:

Take any two numbers 𝑎 and 𝑏 which we would like to multiply together. Let us say 𝑎 = 5 and 𝑏 = 4 . We find these points on the graph of 𝑦 = 𝑥² taking 𝑎 or 𝑏 on either side of the axis:

Next we simply draw a line that connects these two points:

The point where the line intersects the y axis is your answer of a times 𝑏!

Why it works?

For those of you that are interested, here is the maths behind why this works.

The equation of a line is given as:

Now, taking any two numbers 𝑎 and 𝑏 from our graph we have the following coordinates:

The gradient of our line 𝑚 is given as:

Making the equation of our line:

Now to find 𝑐 we substitute a point on the graph (𝑏, 𝑏²), that is 𝑥 = 𝑏 and 𝑦 = 𝑏²:

Leaving us with:

Now we have the equation of the line as:

To find our 𝑦 intercept, we set 𝑥 = 0, giving us:

This shows that the number at the 𝑦 intercept, that is where our line intersects the 𝑦 axis, is the result of 𝑎 times 𝑏!

Thank you very much for reading and I hope you learnt something new!