Interactive linear relationship parameter explorer showing how gradient and y-intercept control line position

Two numbers control infinity

Every straight line — from taxi fares to depreciation — is completely defined by just two parameters: gradient m and y-intercept c. Change one slider and watch the entire line rotate or shift. The maths is simple. The power is absolute.

Linear Control m = 1.0 • c = 0
Drag sliders to reshape the line
y = 1.0x + 0
m = -3 Gradient m = 3
c = -4 Y-Intercept c = 4
Rise per run
+1.0
Starting value
0
Parallel lines are mathematical clones: they share identical gradients but live at different heights. If one line has m = 2, every parallel line also has m = 2, regardless of their y-intercepts. They'll never intersect because they're climbing at exactly the same rate. In real-world terms, this models scenarios where processes grow at the same rate but start from different baselines — think two investment accounts with identical interest rates but different initial deposits.
Know This
The equation y = mx + c isn't just describing a line — it's predicting every single point that line will ever touch, using only two numbers.