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Warm Up
1. Determine if this relation is a function.
2. Find 𝑓(3) if 𝑓 π‘₯ =
π‘₯ 2 βˆ’2
.
π‘₯βˆ’1
3. Find the x-intercept and y-intercept of the graph of
3π‘₯ βˆ’ 5𝑦 = 15. The graph the equation.
4. Find the slope of a line that passes through (3, 5)
and (4, 1).
2.4 Writing Equations of Lines
The slope intercept form of the equation of
a line is 𝑦 = π‘šπ‘₯ + 𝑏 where π‘š is the
___________ and 𝑏 is the _____________.
Slope-Intercept Form
Option 1: Given the slope and yintercept of a line.
4
π‘ π‘™π‘œπ‘π‘’ , 𝑦 βˆ’ π‘–π‘›π‘‘π‘’π‘Ÿπ‘π‘’π‘π‘‘ π‘Žπ‘‘ 4
3
Slope-Intercept Form
Option 2: Given a graph.
y
x
Slope-Intercept Form
Option 3: Given the slope and point
on the line.
1
π‘š = , π‘π‘Žπ‘ π‘ π‘’π‘  π‘‘β„Žπ‘Ÿπ‘œπ‘’π‘”β„Ž 2, 3
2
Slope-Intercept Form
Option 4: Given two points on the
line.
π‘π‘Žπ‘ π‘ π‘’π‘  π‘‘β„Žπ‘Ÿπ‘œπ‘’π‘”β„Ž 2, 3 π‘Žπ‘›π‘‘ (βˆ’1, 2)
Try It On Your Own.
Write an equation of the line.
1. π‘π‘Žπ‘ π‘ π‘’π‘  π‘‘β„Žπ‘Ÿπ‘œπ‘’π‘”β„Ž 0, βˆ’6 π‘Žπ‘›π‘‘ βˆ’4, 10 .
2. π‘π‘Žπ‘ π‘ π‘’π‘  π‘‘β„Žπ‘Ÿπ‘œπ‘’π‘”β„Ž 6, βˆ’2 π‘€π‘–π‘‘β„Ž π‘Ž π‘ π‘™π‘œπ‘π‘’ π‘œπ‘“ βˆ’ 4
Point-Slope Form
The point-slope form of the equation of a line is
𝑦 βˆ’ 𝑦1 = π‘š(π‘₯ βˆ’ π‘₯1 ),
where (π‘₯1 , 𝑦1 ) are the coordinates of a point on
the line and π‘š is the slope of the line.
Point-Slope Form
Option 1: Given the slope and a
point on the line.
π‘š = βˆ’4, π‘‘β„Žπ‘Žπ‘‘ π‘π‘Žπ‘ π‘ π‘’π‘  π‘‘β„Žπ‘Ÿπ‘œπ‘’π‘”β„Ž (6, βˆ’2)
Point-Slope Form
Option 2: Given two points on the
line.
π‘π‘Žπ‘ π‘ π‘’π‘  π‘‘β„Žπ‘Ÿπ‘œπ‘’π‘”β„Ž 2, 3 π‘Žπ‘›π‘‘ (βˆ’1, 5)
Try It On Your Own
Write an equation of the line.
1. π‘π‘Žπ‘ π‘ π‘’π‘  π‘‘β„Žπ‘Ÿπ‘œπ‘’π‘”β„Ž 2, 3 π‘€π‘–π‘‘β„Ž π‘Ž π‘ π‘™π‘œπ‘π‘’ π‘œπ‘“
2. π‘π‘Žπ‘ π‘ π‘’π‘  π‘‘β„Žπ‘Ÿπ‘œπ‘’π‘”β„Ž βˆ’2, βˆ’1 π‘Žπ‘›π‘‘ (3, 4).
1
2
Standardized Testing
Tests like HSAP or the COMPASS love to ask questions
like this…
Which is an equation of the line that passes
through (-2, 7) and (3, -3)?
A. π’š =
𝟏
𝒙
𝟐
βˆ’
πŸ‘
𝟐
B. π’š = βˆ’πŸπ’™ + πŸ‘
C. π’š =
𝟏
𝒙
𝟐
+πŸ–
D. π’š = πŸπ’™ + 𝟏𝟏
Parallel Lines
How do you know if two lines are parallel?
Their SLOPES are the SAME!
𝑦 = 3π‘₯ βˆ’ 1 and 𝑦 = 3π‘₯ + 13
𝑦=
1
π‘₯
2
and 𝑦 =
1
π‘₯
2
+1
Example
Write an equation of a line that passes through
𝟏
(12, 0) and is parallel to π’š = βˆ’ 𝒙 βˆ’ πŸ‘.
𝟐
Write an equation of a line that passes through (0, 9)
𝟐
and is parallel to π’š = 𝒙 βˆ’ 𝟏𝟎.
πŸ‘
Perpendicular Lines
How do you know if two lines are perpendicular?
Their SLOPES are the NEGATIVE RECIPROCALS!
𝑦 = 3π‘₯ βˆ’ 1 and 𝑦 =
𝑦 = βˆ’2π‘₯ and 𝑦 =
1
βˆ’ π‘₯
3
1
π‘₯
2
+ 13
+1
Example
Write an equation of a line that passes through
𝟐
(5, -6) and is perpendicular to π’š = βˆ’ 𝒙 + πŸ•.
πŸ‘
Write an equation of a line that passes through
(6, -1) and is parallel to π’š = πŸ‘π’™ βˆ’ 𝟐.
Summary
Slope-Intercept Form:
Point-Slope Form:
Parallel Lines:
Perpendicular Lines:
Homework!!! YAY! 
Lesson 2.4
Page 87
#’s 9, 13, 15, 17-19, 23, 24 and 32