Find the Equation of a Line Parallel to Another Line in Point-Slope and Slope-Intercept Form | Summary and Q&A

TL;DR

Learn how to find a line's equation using point-slope and slope-intercept forms.

Key Insights

• 😥 Point-slope form: y-y1=m(x-x1) with point and slope.
• 🫥 Parallel lines have the same slope.
• 💁‍♂️ Slope-intercept form gives y=mx+b, helpful for solving y.

Transcript

in this problem we have to find the equation of the line given some information in point-slope form and slope-intercept form so first start by writing down the point-slope form of a line so the formula the point-slope formula is y minus y1 equals m parenthesis x minus x1 so all we have to do is figure out our point x1 y1 and our slope which is m so... Read More

Questions & Answers

Q: What is the point-slope form of a line and how is it used in finding the equation?

The point-slope form is y-y1=m(x-x1), where (x1,y1) is the point and m is the slope. Plug in these values to find the line's equation.

Q: Why does a parallel line have the same slope, and how does it help in finding the equation?

Parallel lines have identical slopes. Knowing the slope of a line parallel to the one given helps determine the slope of the line to be found.

Q: How does distributing the slope in the slope-intercept form help in solving for y?

Distributing the slope yields y+constant=slopex. By isolating y, you get y=slopex+constant, which is the slope-intercept form of a line.

Q: Why is it important to determine whether to use the point-slope or slope-intercept form in finding a line's equation?

Point-slope form is useful when a point and slope are given, while slope-intercept form is used when simplifying a line's equation to y=mx+b.

Summary & Key Takeaways

• Point-slope form: y-y1=m(x-x1) with given point (x1,y1) and slope m.

• Slope of parallel line is the same; use given point to plug into point-slope form.

• Slope-intercept form: y=mx+b, solve for y by distributing slope and simplifying.