Move points A and B around the coordinate plane with the sliders. There's exactly one line through any two points, and its slope and equation get calculated live. Use the parallel and perpendicular buttons to explore the relationship between their slopes too.
Slope = (change in y) รท (change in x) = (yโโyโ) / (xโโxโ). Once you know two points, you can find the slope, and once you have a slope and one point, you can build the equation of the line.
Press "Show parallel line" below, and a line through the gray point R appears that has the exact same slope as line AB. Press "Show perpendicular line," and a line appears whose slope multiplies with AB's to give โ1.