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Equation Of The Line

FIND THE EQUATION OF A LINE

Procedure for finding the equation of Diagonal Lines

1. Find slope (m)

a. Given

b. Calculate using the slope formula _________________

c. Given the equation of a line and a parallel relationship slopes are equal

d. Given an equation of a line and a perpendicular relationship the slopes are opposite reciprocals

2. To find the equation of a line,

a. In any form other than slope intercept given information using y - y

= m(x - x

), substitute (x,y) and

slope, then format

b. In slope-intercept form, given information using y = mx + b, substitute (x,y) and slope. Solve for b. Final

equation, substitute the m and b into y=mx + b

Examples

1. Find the equation of the line given m=4/3 through (2,3)

2. Find the equation of the line in slope intercept form with m=2 through (5, -1)

3. Find the equation of the line through points (2,4) and (1,5) in standard form



5 4



 



Step 1: find the slope

1 2

Step 2: substitute slope and point into the point-slope equation of the line

  



    

(



 , so after distributing the -1 and manipulating the equation…

Step 3: In standard form means

ax by c

 

x y

4. Find the equation of the line through ( -3, -2) and parallel to 3x + 4y = 5

5. Find the equation of the line in slope intercept form through (4, -1) and perpendicular to y = 1/3 x - 4

Equation Of The Line