Point-Slope Form
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
Point-slope form is a way of expressing a linear equation based on a specific point on the line and its slope. The formula is:
where:
(x1, y1) is a point on the line,
m is the slope of the line.
Key Features:
Point: The coordinates (x1, y1) represent a known point through which the line passes.
Slope: The slope m indicates the rate of change of y with respect to x. It describes how steep the line is.
Usage: Point-slope form is particularly useful for writing the equation of a line when you know a point on the line and its slope, making it straightforward to derive the equation without needing to find the y-intercept first.
Example:
If a line has a slope of 2 and passes through the point (3, 4), the equation in point-slope form would be:
y - 4 = 2(x - 3)
This form can be converted to slope-intercept form or standard form if needed.