Writing Linear Equations of Parallel and Perpendicular Lines - Algebra | Summary and Q&A

TL;DR

Learn how to write the equation of a line that passes through a given point and is either parallel or perpendicular to another given line.

Key Insights

• 🫥 The equation of a line requires a point and a slope.
• 🫥 Parallel lines have the same slope, while perpendicular lines have negative reciprocal slopes.
• 😥 The point-slope formula is used to write the equation in point-slope form.
• 💁 Converting to slope-intercept form involves distributing the slope, simplifying, and solving for y.
• 😥 Checking the equation by substituting a point ensures accuracy.
• 🫥 Understanding the symbols for parallel and perpendicular lines helps identify their relationships.
• 😃 Slope-intercept form (y = mx + b) provides a clear representation of the equation.

Transcript

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Questions & Answers

Q: How do we determine the slope of a line parallel to a given line?

For parallel lines, the slope is the same as the given line. In slope-intercept form (y = mx + b), the coefficient of x represents the slope. Therefore, we use the same coefficient of x for the parallel line.

Q: What is the slope of a line perpendicular to a given line?

Perpendicular lines have slopes that are negative reciprocals of each other. To find the slope of a line perpendicular to a given line, we change the sign of the slope and flip the fraction.

Q: What is the point-slope formula used for?

The point-slope formula (y - y1 = m(x - x1)) is used to write the equation of a line that passes through a given point (x1, y1) and has a given slope (m). It provides a straightforward way to represent the equation of a line.

Q: How can we check if we have the correct equation of a line?

To check if a point lies on a line, we can substitute the coordinates of the point into the equation of the line. If the resulting values on both sides of the equation are equal, then the point is on the line.

Summary & Key Takeaways

• To write the equation of a line, we need a point and a slope. For parallel lines, the slope is the same as the given line, while for perpendicular lines, the slope is the negative reciprocal of the given line.

• Using the point-slope formula (y - y1 = m(x - x1)), we can plug in the given point and slope to obtain the equation in point-slope form.

• To convert the equation to slope-intercept form (y = mx + b), we distribute the slope, combine like terms, and solve for y.