This document provides instructions for writing the equation of a line given two points in both slope-intercept and standard form. It explains how to find the slope between two points and use the point-slope formula to write the equation in slope-intercept form. It then shows how to take that equation and rearrange it to write it in standard form, ensuring the leading coefficient is positive and there are no fractions or common factors. An example is worked through step-by-step to demonstrate these processes.

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