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 pointslope formula is used to write the equation in pointslope form.
 💁 Converting to slopeintercept 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.
 😃 Slopeintercept form (y = mx + b) provides a clear representation of the equation.
Transcript
write the equation of the line that passes through the point two comma three and is parallel to the line y equals four x minus three how can we solve this problem well in order to write the equation of the line we need at least two things the slope and the point we already have the point all we need to do is find a slope and the formula that we're ... Read More
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 slopeintercept 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 pointslope formula used for?
The pointslope 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 pointslope formula (y  y1 = m(x  x1)), we can plug in the given point and slope to obtain the equation in pointslope form.

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