Point-slope formula

Definition

The point-slope formula is a method for finding the equation of a line when you know the slope and one point on the line. It is written as $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a given point and $m$ is the slope.

5 Must Know Facts For Your Next Test

1. The point-slope formula can be used to derive other forms of linear equations, such as slope-intercept form.
2. To use the formula, you need exactly one point on the line and the slope of the line.
3. The formula is particularly useful for writing equations when dealing with non-horizontal or non-vertical lines.
4. You can transform an equation from point-slope form to standard form by rearranging terms.
5. The slope ($m$) in the formula represents how steep the line is and its direction (positive for upward, negative for downward).

Review Questions

• What information do you need to use the point-slope formula?
• How do you convert an equation from point-slope form to slope-intercept form?
• If given a point (3,4) and a slope of -2, what is the equation of the line using point-slope form?

Related terms

Slope-Intercept Form: A linear equation format written as $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Standard Form: A way to write linear equations in the format $Ax + By = C$, where A, B, and C are integers.

Slope: A measure of how steep a line is; calculated as rise over run ($\frac{\Delta y}{\Delta x}$).