There are many different ways that you can express the equation of a line. There is the slope intercept form , standard form and also this page's topic-point slope form. Each one expresses the equation of a line, and each one has its own pros and cons. Point Slope form, this page's topic, makes it easy to find the line's equation when you only know the slope and a single point on the line(see example 1).. Point slope form is also the quickest method for finding the equation of line given two points (see example 2).
Definition of the Point Slope Form Equation
The Point Slope Form Formula:
Example and Non Example Equations
Problem 1)
Identify which equations below are in point slope form
Equation 1: 2x + 2y =6
Equation 2: y - 5 = 3(x -2)
Equation 3: y =2x + 3
Equation 4: y + 3 = 3(x - ½)
Answer
Equation 2 and equation 4 are the only ones in point slope form.
Equation 1 is in Standard Form
Equation 3 is in Slope intercept form
Problem 2)
Which equations below are in point slope form
Equation 1: y − 2 = 3(x − 4)
Equation 2: y + 5= (x − 4)
Equation 3: y = 3(x − 4) +2
Equation 4: y − 2 = 3(x − 4)
Answer
Equation 1, 2 and equation 4 are the in point slope .
How to Solve common point slope form questions
Example 1: Find equation given slope and 1 point
Write the point slope equation of a line with slope 3 that passes through the point (-2, 5).
1)Substitute slope for 'm' and the coordinates for x_{1} and y_{1} into the formula
y − y_{1}= m(x − x_{1})
y − 5 = 3(x − -2)
y − 5 = 3(x + 2 )
Yes , it really is that easy to write the equation of a line in point slope form when you know its slope and 1 point on the line! . This should be a real relief to those of you who are used to doing this with slope intercept form , which would require 2 more steps (i.e. substitute a point and solve for b').
Example 2: Find equation given 2 points
Write the point slope equation of a line that goes through the points (1 , 7 ) and ( 5 , 19 ) .