Transcript Document

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
If you are given the slope and y-intercept
of a line, you can find an equation of the
line by substituting the values of π‘š and 𝑏
into the slope-intercept form.
1. π‘ π‘™π‘œπ‘π‘’
4
, π‘π‘Žπ‘ π‘ π‘’π‘ 
3
π‘‘β„Žπ‘Ÿπ‘œπ‘’π‘”β„Ž 0, 4
Examples
Sometimes it is necessary to calculate the
slope before you can write an equation.
Write an equation in slope-intercept form
for the line.
Try two 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.
Using a previous example:
Write an equation of a line through 6, βˆ’2 with
a slope of 4 using point-slope form.
Try two 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‘“
1
2
2. π‘π‘Žπ‘ π‘ π‘’π‘  π‘‘β„Žπ‘Ÿπ‘œπ‘’π‘”β„Ž βˆ’2, βˆ’1 π‘€π‘–π‘‘β„Ž π‘Ž π‘ π‘™π‘œπ‘π‘’ π‘œπ‘“ βˆ’ 3.
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
Equations of a Line
What if you are asked to write the equation
of a line given two points?
(-8, -5) and (-3, 10)
What would you have to do?
1.
Find the SLOPE (π‘š)
2.
Use point-slope form to find the equation
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:
Equations of a line: (1)
(2)
Parallel Lines:
Perpendicular Lines:
Homework!!! YAY! 
Lesson 2.4
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#’s 9, 13, 15, 17-19, 23, 24 and 32