How can a shape be described with numbers?
I think, therefore I am.
René Descartes was a French philosopher and mathematician who connected algebra with geometry. He showed that a point could be written as two numbers, a shape could be written as an equation, and an equation could be solved to answer a question about the shape.
Foundation: plot it
Every point on the page is a pair of numbers, (x, y). Plot a few points and join them — the pattern they make is the shape.
Deeper: write the rule
A straight line through those points follows one rule: y = mx + c. m is how steep the line is; c is where it crosses the y-axis.
Extension: use the rule
Two lines meet where their equations agree. Solve y = mx + c for two lines at once and you've found exactly where they cross — no drawing required.
The language gets more precise with depth, but it is the same idea throughout: numbers describe the shape, and the shape answers the question.
Move the model, make a prediction
As the angle increases towards 90°, what happens to the gradient m?
Check the idea
A line has equation y = 3x + 2. What is its gradient?
Choose an answer to see explanatory feedback.
Sample explanation
Why the equation comes before the graph
A diagram shows what the line looks like, an equation lets you calculate exactly where it goes, and a short video can walk through both together. The lesson keeps all three beside the same idea rather than scattering them across separate pages.
See also
Reading a graph like this is exactly the skill used in Chemistry: visualising energy changes — plotting how a quantity changes against time or reaction progress.