Point-slope formula

Definition

The point-slope formula is a method used to find the equation of a line given a point on the line and its slope. It is expressed as $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line and $m$ is the slope.

5 Must Know Facts For Your Next Test

1. The point-slope form is useful for writing the equation of a line when you know one point and the slope.
2. It can be easily converted to slope-intercept form ($y = mx + b$) by solving for $y$.
3. The formula emphasizes the relationship between changes in $x$ and corresponding changes in $y$.
4. Any linear equation can be represented using point-slope form if at least one point on the line and the slope are known.
5. $(x_1, y_1)$ represents any specific point through which the line passes.

Review Questions

• What information do you need to use the point-slope formula?
• How would you convert an equation from point-slope form to slope-intercept form?
• $$(x_1, y_1)$$ are coordinates of what in the context of the point-slope formula?

Related terms

Slope-Intercept Form: A way to express linear equations as $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Standard Form: A linear equation written as $Ax + By = C$, where A, B, and C are integers.

$(x,y)$ Coordinates: An ordered pair representing a specific location on a Cartesian plane.