Equation of a Straight Line – y = mx + c
Every straight (non-vertical) line on the coordinate plane can be described by a single equation: y = mx + c. Here, m is the gradient (how steep the line is), and c is the y-intercept (where it crosses the y-axis). Once you know m and c, you know absolutely everything about that line – you could redraw it perfectly without ever seeing the original graph.
This equation is one of the most useful tools in all of mathematics precisely because it connects an algebraic expression directly to a geometric picture – exactly the fusion Descartes and Fermat pioneered when they founded coordinate geometry in the 1630s.
Reading y = mx + c
In y = mx + c: m is the gradient (steepness/direction), and c is the y-intercept (where the line crosses the y-axis).
Gradient m = −2. y-intercept c = 7.
Substitute x = 3: y = 2(3) − 5 = 1. This matches the given y-value, so the point does lie on the line.
Real-Life Application
- Pricing plans: a fixed fee plus a per-unit rate is a straight-line equation.
- Travel graphs: constant-speed journeys are modelled by straight lines.
- Conversion formulas: many unit conversions (e.g. temperature) follow y = mx + c.
Key Takeaways
- y = mx + c describes every non-vertical straight line.
- m is the gradient; c is the y-intercept.
- A point lies on the line only if its coordinates satisfy the equation exactly.
Practice: Equation of a Straight Line
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