Writing the Equation of Line Given Two Points
- 1. Writing the Equation of a Line Slope-intercept and Standard Forms
- 2. Objective: Given two points, write the equation of a line in both slope-intercept and standard forms. Standard Form
- 3. Point-Slope Form m is the slope (x1, y1) is one of the points on the line.
- 4. Example Write the equation of the line that passes through the points (1, 4) and (-2, -5) in both slope-intercept and standard forms. First, find the slope. (CC BY-NC 2.0)
- 5. Use Point-Slope Form Use m=3 and one point. We will choose (1,4).
- 6. Now solve for y… Distribute Add 4 to both sides Simplify This is the slope-intercept form of the line.
- 7. Standard Form (Ax+By = C) Three Conditions: There are no fractions. The leading coefficient, A, is positive. A, B, and C have no common factors.
- 8. Write the equation in standard form (Ax+By = C) Subtract 3x on both sides This matches Ax+By = C Next step: Check the 3 conditions…
- 9. Check the Conditions… Three Conditions: There are no fractions – This condition is already met. The leading coefficient, A, is positive – multiply both sides of the equation by -1. A, B, and C have no common factors – This condition is already met.
- 10. Final Answer! Equation in standard form:
- 11. The Graph…just for fun Here is the graph of y=3x+1 You can see that the line passes through our original points (1,4) and (-2, -5)
- 12. Photo Credit The photo “Downhill Skiing in Kajaani, Finland” is © 2005 Visit Finland, used under a Creative Commons Attribution-NonCommercial 2.0 Generic license: http://creativecommons.org/licenses/bync/2.0/deed.en