Three costumes, one line
The same line owns three costumes. Standard form, — where is the number in front of , the number in front of , and the plain number on the right — hides the slope in those coefficients: — read aloud, m equals negative A over B. That minus sign is not decoration; it is the toll for moving across the equals sign. Forgetting it is this lesson's headline mistake — cheap to avoid, expensive to make.
Two more tools for the belt. The x-intercept is where a line touches down on the x-axis: set and out falls , with and still meaning what they did last lesson — the starting height and the slope. And point-slope form, — y equals y-one, plus m times x minus x-one — builds y from any point you know: is that known point, is the spot you are asking about, and is the height there. Start where you stand, then let the slope carry you the rest of the trip.
- = Slope
- = Coefficient of x
- = Coefficient of y
- = x-intercept (length)
- = Slope
- = y-intercept (length)
- = y-coordinate (length)
- = Known point y-coordinate (length)
- = Slope
- = x-coordinate (length)
- = Known point x-coordinate (length)