The Equation of a Straight Line
Every straight line you can draw has the same tidy equation:
y = mx + c
Just two numbers fix the whole line. The number m is the
gradient — how steeply the line tilts — and c is
the y-intercept — the height at which it crosses the
y-axis. (The gradient is exactly the
gradient you have
already measured as rise over run.)
For a straight line written as y = mx + c:
- m is the gradient — the steepness of the line;
- c is the y-intercept — where the line cuts the y-axis;
- a bigger m makes the line steeper;
- changing c slides the whole line straight up or down.
Drive the line yourself
Pull the two sliders. Watch m tilt the line and
c slide it up and down without changing its tilt.
Reading a line off its equation
Once a line is in this form, its two facts read straight off. For
y = 2x + 3 the gradient is m = 2 and the
y-intercept is c = 3, so the line climbs
two units for every one across and crosses the axis at (0, 3). To
find y at any x, substitute it in: at
x = 4, y = 2(4) + 3 = 11.