Lines in the Plane and Slope
The simplest mathematical model for relating two variables is the linear equation (Slope-intercept form). This equation is called Linear because its graph is a line. is the slope and is the y-intercept.
Finding the slope
For instance, suppose you want to find the slope of the line passing through the distinct points and .
Exercises Find the slope of the line passing through the distinct points below
Writing the linear equation given a slope and a point on the line
Point-Slope Form of the Equation of a Line The equation of the line with slope passing through the point is
Notice: In order to write this equation, we need a point and a slope given
Exercises Find the equation of the line line given the information below
1) slope and goes through
|Apply the formula with , and to get the result|
Writing the linear equation given two points on the line
Given two point and are on the line. To find the equation of this line:
First, use the formula to find the slope
Then, apply the point-slope formula with the slope we just found and one of the given points.
Exercises Find the equation of the line passing through the distinct points below
|Apply the point-slope formula with slope and the given point ( I choose in this case, but will give the same result) to get|
A vertical line goes through has equation of the form where is any constant.
This page were made by Tri Phan