Point-slope equation

Definition

The point-slope equation of a line is given by $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line and $m$ is the slope. It is useful for writing the equation of a line when you know one point and the slope.

5 Must Know Facts For Your Next Test

1. The general form of the point-slope equation is $y - y_1 = m(x - x_1)$.
2. It can be derived from the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ by rearranging terms.
3. You can convert the point-slope form to slope-intercept form by solving for $y$.
4. The point-slope form is particularly useful in calculus for finding tangent lines to curves.
5. A common test problem involves using given points and slopes to write or identify the correct point-slope equation.

Review Questions

• What information do you need to write an equation in point-slope form?
• How can you convert a point-slope equation to slope-intercept form?
• Given two points on a line, how would you use them to write an equation in point-slope form?

Related terms

Slope:

The rate at which $y$ changes with respect to $x$, calculated as $m = \frac{\Delta y}{\Delta x}$.

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

Linear Equation: An algebraic equation in which each term is either a constant or the product of a constant and a single variable.