Two-Point Formula

Definition

The two-point formula is a mathematical equation used to find the equation of a line given two distinct points on that line. It allows you to determine the slope and y-intercept of the line, which are the necessary components to write the equation in slope-intercept form.

5 Must Know Facts For Your Next Test

1. The two-point formula is $y_2 - y_1 / x_2 - x_1$ to calculate the slope of a line.
2. Once the slope is known, the y-intercept can be found by plugging in the coordinates of one of the given points into the slope-intercept form equation.
3. The two-point formula is commonly used when the equation of a line is not provided, and only the coordinates of two distinct points on the line are given.
4. Knowing the slope and y-intercept allows you to write the equation of the line in slope-intercept form, $y = mx + b$.
5. The two-point formula is a foundational concept for finding the equation of a line, which is a key skill in the topic of 3.3 Find the Equation of a Line.

Review Questions

• Explain how the two-point formula is used to find the equation of a line.
  • The two-point formula is used to calculate the slope of a line given the coordinates of two distinct points on that line. The formula is $y_2 - y_1 / x_2 - x_1$. Once the slope is known, the y-intercept can be found by plugging the coordinates of one of the given points into the slope-intercept form equation, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. With the slope and y-intercept, the full equation of the line can be written in slope-intercept form.
• Describe the relationship between the two-point formula and the slope-intercept form of a linear equation.
  • The two-point formula is directly connected to the slope-intercept form of a linear equation, $y = mx + b$. The two-point formula is used to calculate the slope, $m$, of the line. Once the slope is known, the y-intercept, $b$, can be found by plugging the coordinates of one of the given points into the slope-intercept equation. Together, the slope and y-intercept allow the full equation of the line to be written in the standard slope-intercept form, which is a key skill in the context of finding the equation of a line.
• Analyze how the two-point formula and the concept of slope work together to determine the equation of a line.
  • The two-point formula and the concept of slope are essential for finding the equation of a line. The two-point formula allows you to calculate the slope of the line by using the coordinates of two distinct points. Knowing the slope, $m$, is crucial because it is one of the two key components needed to write the equation in slope-intercept form, $y = mx + b$. The other component, the y-intercept $b$, can then be found by plugging the coordinates of one of the given points into the slope-intercept equation. By leveraging the two-point formula to determine the slope and then using that slope to find the y-intercept, you can fully construct the equation of the line, which is the ultimate goal in the context of 3.3 Find the Equation of a Line.

Related terms

Slope: The rate of change or steepness of a line, calculated as the rise over the run between two points.

Y-Intercept: The y-coordinate of the point where a line intersects the y-axis, representing the constant term in the equation of a line.

Slope-Intercept Form: The standard form of a linear equation written as $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.