# 2.4 Notes

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```Advanced Algebra Notes
Section 2.4: Write Equations of Lines
Given slope and y-intercept b
Use slope-intercept form
π¦ = ππ₯ + π
Given slope and a point (π₯, π¦)
Use point slope form
π¦ − π¦1 = π π₯ − π₯1
Given points (π₯1 , π¦1 ) and (π₯2 , π¦2 )
First use the slope formula to find m.
πππ π ππ£ππ ππ’π πππ‘π  π‘βπ πππ ππππ! Then use point-slope form with either point
πππ π (π¦)
ππ π π ππππ πππππ’ππ π‘π ππππ π (π ππππ)
π=
πβππ πππ‘βππ πππππ’ππ π€πππ π€πππ!
ππ’π (π₯)
Example 1
Write an equation of the line shown.
πΈππ’ππ‘πππ ππ π ππππ
π¦ = ππ₯ + π
πβππ‘ ππ  ππ’π π ππππ? πβπππ
ππππ  π‘βπ ππππβ π π‘πππ‘ ππ π‘βπ
π¦ − ππ₯ππ ?
3
π¦ = π₯ + (−2)
4
Example 2
Write an equation of the line that passes through (5,4) and has a slope of −3.
π¦ − π¦1 = π(π₯ − π₯1 )
πππππ‘ − π ππππ ππππ
πππ’π ππ π‘βπ πππ£ππ π£πππ’ππ !
π¦ − 4 = −3(π₯ − 5)
π¦ − 4 = −3(π₯ − 5)
π¦ − 4 = −3π₯ + 15
π¦ = −3π₯ + 19
Example 3
Write an equation of the line that passes through (−2,3) and is
Parallel to the line π¦ = −4π₯ + 1
πΏππππ  π‘βππ‘ πππ ππππππππ βππ£π π‘βπ π πππ π ππππ!
π¦ = −4π₯ + π
−5 = π
π¦ = −4π₯ − 5
3 = −4(−2) + π
Perpendicular to the line π¦ = −4π₯ + 1
πΏππππ  π‘βππ‘ πππ ππππππππππ’πππ βππ£π πππππ ππ‘π ππππππππππ π ππππ!
1
1
π¦ − π¦1 = −4(π₯ − π₯1 )
1
7
π¦ = π₯+ +3
π¦= π₯+
1
4
2
4
2
π¦ − 3 = (π₯ + 2)
4
Example 4
Write an equation of the line that passes through (5, −2) and (2,10)
πΉπππ π‘ ππππ π‘βπ π ππππ!
10 − (−2)
π=
2−5
12
π=
−3
π = −4
πππ π ππ£ππ ππ’π πππ‘π  π‘βπ πππ ππππ!
π¦ − π¦1 = −4(π₯ − π₯1 )
πΈππ‘βππ πππππ‘ π€πππ π€πππ!
π¦ − (−2) = −4(π₯ − 5)
π¦ + 2 = −4π₯ + 20
π¦ = −4π₯ + 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.
π₯ = # ππ π¦ππππ
π¦ = # ππ ππππ‘πππππππ‘π
π¦ = ππ₯ + π
π¦ = (.086)π₯ + π
πβππ‘ ππ  π‘βπ πππ‘πππ πβππππ ππππ 1993 π‘π 2003
… ππ ππ‘βππ π€ππππ  … π‘βπ π ππππ!
2.86 − 2.00
π=
10 − 0
π = .086
2.00 ππ  π‘βπ ππππ‘πππ ππππ’ππ‘
π¦ = (.086)π₯ + 2.00
Closing: How do you write an equation of a line?
πππ’ π’π π π‘βπ π ππππ, π¦ − πππ‘ππππππ‘ πππ π πππ£ππ πππππ‘
ππππ£π πππ π‘βπ π ππππ
π·πππππ π€βππβ πππππ’ππ π€ππππ  πππ π‘ …
πππππ − πππ‘ππππππ‘
π¦ = ππ₯ + π
πππππ‘ − π ππππ ππππ
π¦ − π¦1 = π(π₯ − π₯1 )
HOMEWORK
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