Equation of a Straight Line
Simple Explanation
Every non-vertical straight line can be written as y = mx + c, where m is the slope and c is the y-intercept — the height where the line crosses the y-axis.
Why Do We Need It?
This equation lets you describe an entire line — every one of its infinite points — with just two numbers, and predict a y-value for any x-value on it.
See It
A coordinate plane showing a line through two draggable points, its slope, and where it crosses each axis
Formula
Equation of a Straight Line
y = mx + c
Describes every point on a non-vertical straight line, using its slope and y-intercept.
- m
- — the slope of the line
- c
- — the y-intercept — where the line crosses the y-axis
- x, y
- — the coordinates of any point on the line
When to use it: Whenever you need to write down, graph, or predict values along an entire straight line, not just one point on it.
Worked Example
Find the equation of a line
Find the equation of the line with slope 3 that passes through (2, 11).
Why Does This Work?
Every point on the line must satisfy y = mx + c, so plugging in one known point pins down the only remaining unknown, c — after that, the equation describes every other point on the line too.
Real-Life Example
Predicting cost from usage
A taxi fare might be a fixed starting charge plus a set rate per kilometre.
That is y = mx + c in disguise: c is the starting charge, m is the cost per kilometre (the slope), and y is the total fare for x kilometres.
Practice
In the line y = 4x − 7, what is the y-intercept?
EasyA line has slope 2 and passes through (3, 10). What is its y-intercept, c?
MediumCommon mistake
Confusing which number is the slope and which is the intercept when reading y = mx + c — m always multiplies x; c stands alone.
Quick Review
- y = mx + c describes any straight (non-vertical) line.
- m is the slope; c is the y-intercept.
- Substitute one known point to solve for c once you know m.