How to Write Equations for Parallel and Perpendicular Lines

TL;DR

To write the equation of a line parallel to a given line, use the same slope and substitute the given point into y = mx + b to find the y-intercept. For a perpendicular line, flip the slope's fraction and change its sign, then solve for the y-intercept using the same point.

Transcript

in this video we're going to focus on writing equations of lines that are parallel and perpendicular to a given line but pass them to a point so let's say if we have the equation y is equal to 2x plus one and we wanna write the equation of a line that's parallel to the line y equals two x plus one and that passes through the point one comma five ho... Read More

Key Insights

• 😃 Slope-intercept form (y = mx + b) is useful for writing line equations.
• 🫥 Parallel lines have the same slope, while perpendicular lines have negative reciprocal slopes.
• 🏙️ Substitute given point coordinates to solve for the y-intercept and complete the line equation.
• 🫥 Flipping the slope and changing its sign gives the slope for a perpendicular line.

Questions & Answers

Q: How do I write the equation of a line parallel to a given line?

To write the equation of a line parallel to a given line, use the same slope, and solve for the y-intercept by substituting the coordinates of a given point. Plug the slope and y-intercept into the slope-intercept form equation.

Q: What is the process for writing the equation of a line perpendicular to a given line?

For a line perpendicular to a given line, flip the slope and change its sign. Then, solve for the y-intercept using a given point. Plug the new slope and y-intercept into the slope-intercept form equation to write the line's equation.

Q: What is the slope-intercept form of a line equation?

The slope-intercept form of a line equation is y = mx + b, where m represents the slope and b represents the y-intercept.

Q: Can you provide an example of writing the equation of a line parallel to a given line?

Sure! Consider the line y = 2x + 1. To write the equation of a parallel line passing through the point (1, 5), we keep the slope as 2 and solve for the y-intercept (b). Substituting x = 1 and y = 5, we find b = 3. Therefore, the equation of the line is y = 2x + 3.

Summary & Key Takeaways

• The slope-intercept form of a line equation is y = mx + b, where m represents the slope and b represents the y-intercept.

• To write the equation of a line parallel to a given line, use the same slope and solve for the y-intercept using a given point.

• To write the equation of a line perpendicular to a given line, flip the slope and change its sign, then solve for the y-intercept using a given point.