Writing the Equation of

a Line

Slope-intercept and Standard Forms

Objective: Given two points, write the equation of a

line in both slope-intercept and standard forms.

Standard Form

Point-Slope Form

m is the slope (x1, y1) is one of the points on the line.

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)

Use Point-Slope Form Use m=3 and one point. We will choose

(1,4).

This is the slope-intercept form of the line.

Distribute

Add 4 to both sides

Simplify

Now solve for y…

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.

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…

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.

Final Answer! Equation in standard form:

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)

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/by-nc/2.0/deed.en