Lines & Linear Systems
The straight line is the first graph you ever meet — and the one every other graph is built from. Slide its slope and intercept, drop in a second line, and find exactly where they cross. Grade 9–10.
Two numbers describe a line
Every non-vertical line is just y = m·x + b. The slope m is how steep it is — rise over run, how far y climbs each time x moves one step right. The intercept b is where the line crosses the y-axis. Change those two numbers and you can draw any straight line there is.
Tilt it, slide it, cross it 📈
Drag the round dot to tilt a line; drag the square dot to slide it up and down. Switch on a second line to make a system — the crossing point is the solution. Or flip to Two points for slope, distance and midpoint.
Two lines, one question
A pair of lines is a system of equations, and "solving" it just means finding the point that sits on both lines at once:
One solution
Different slopes → the lines cross exactly once. That crossing point (x, y) is the one pair of numbers that makes both equations true.
None, or infinitely many
Same slope, different intercept → parallel, they never meet, no solution. Same slope and intercept → it's the same line, so every point is a solution.
Between two points
Switch to Two points mode and drag A and B. The same rise-over-run gives the slope; the straight-line distance is the Pythagorean theorem in disguise √(Δx² + Δy²); and the midpoint is simply the average of the coordinates — the exact halfway mark, marked in purple.