The Slope (or gradient) of a line is a measure of its steepness and direction. It is denoted by m.
Conditions: Parallel lines have equal slopes (m1 = m2). Perpendicular lines have a product of slopes equal to -1 (m1 · m2 = -1).
When two lines with slopes m1 and m2 intersect, the acute angle α between them is given by:
Depending on the information available, we use different forms to represent a straight line in the Cartesian plane.
| Form Name | Equation | Given Information |
|---|---|---|
| Slope-Intercept Form | y = mx + c | Slope (m) and y-intercept (c). |
| Point-Slope Form | y - y1 = m(x - x1) | Slope (m) and a point (x1, y1). |
| Two-Point Form | y - y1 = (y2 - y1) / (x2 - x1)(x - x1) | Two points (x1, y1) and (x2, y2). |
| Intercept Form | (x) / (a) + (y) / (b) = 1 | x-intercept (a) and y-intercept (b). |
The perpendicular distance d from a point (x1, y1) to a line Ax + By + C = 0 is calculated as:
Distance between two parallel lines Ax + By + C1 = 0 and Ax + By + C2 = 0 is:
Q: How do I find the slope of a line given in general form Ax + By + C = 0?
A: Convert it to y = mx + c form. The slope is m = -A/B.
Q: What is the slope of the x-axis and y-axis?
A: The x-axis has a slope of 0 (tan 0°). The y-axis has an undefined slope (tan 90°).