Advanced Algebra Notes
Section 2.4: Write Equations of Lines
Given slope and y-intercept b
Use slope-intercept form
 =  + 
Given slope and a point (, )
Use point slope form
 − 1 =   − 1
Given points (1 , 1 ) and (2 , 2 )
First use the slope formula to find m.
    ℎ  ! Then use point-slope form with either point
 ()
      ()
=
ℎ ℎ   !
 ()
Example 1
Write an equation of the line shown.
   
 =  + 
ℎ   ? ℎ
 ℎ ℎ   ℎ
 − ?
3
 =  + (−2)
4
Example 2
Write an equation of the line that passes through (5,4) and has a slope of −3.
 − 1 = ( − 1 )
 −  
  ℎ  !
 − 4 = −3( − 5)
 − 4 = −3( − 5)
 − 4 = −3 + 15
 = −3 + 19
Example 3
Write an equation of the line that passes through (−2,3) and is
Parallel to the line  = −4 + 1
 ℎ   ℎ ℎ  !
 = −4 + 
−5 = 
 = −4 − 5
3 = −4(−2) + 
Perpendicular to the line  = −4 + 1
 ℎ   ℎ   !
1
1
 − 1 = −4( − 1 )
1
7
 = + +3
= +
1
4
2
4
2
 − 3 = ( + 2)
4
Example 4
Write an equation of the line that passes through (5, −2) and (2,10)
  ℎ !
10 − (−2)
=
2−5
12
=
−3
 = −4
    ℎ  !
 − 1 = −4( − 1 )
ℎ   !
 − (−2) = −4( − 5)
 + 2 = −4 + 20
 = −4 + 18
Example 5
In the school year ending in 1993, 2.00 million females participated in U.S.
high school sports. By 2003, the number had increased to 2.86 million. Write
a linear equation that models female sports participation.
 = #  
 = #  
 =  + 
 = (.086) + 
ℎ  ℎ  ℎ  1993  2003
…  ℎ  … ℎ !
2.86 − 2.00
=
10 − 0
 = .086
2.00  ℎ  
 = (.086) + 2.00
Closing: How do you write an equation of a line?
  ℎ ,  −     
  ℎ 
 ℎℎ    …
 − 
 =  + 
 −  
 − 1 = ( − 1 )
HOMEWORK
#1 − 19