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