Transcript Document

Warm Up
1. Determine if this relation is a function.
2. Find 𝑓(3) if 𝑓 𝑥 =
𝑥 2 −2
.
𝑥−1
3. Find the x-intercept and y-intercept of the graph of
3𝑥 − 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 = 𝑚𝑥 + 𝑏 where 𝑚 is the
___________ and 𝑏 is the _____________.
Slope-Intercept Form
Option 1: Given the slope and yintercept of a line.
4
𝑠𝑙𝑜𝑝𝑒 , 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 𝑎𝑡 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
𝑚 = , 𝑝𝑎𝑠𝑠𝑒𝑠 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 2, 3
2
Slope-Intercept Form
Option 4: Given two points on the
line.
𝑝𝑎𝑠𝑠𝑒𝑠 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 2, 3 𝑎𝑛𝑑 (−1, 2)
Try It On Your Own.
Write an equation of the line.
1. 𝑝𝑎𝑠𝑠𝑒𝑠 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 0, −6 𝑎𝑛𝑑 −4, 10 .
2. 𝑝𝑎𝑠𝑠𝑒𝑠 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 6, −2 𝑤𝑖𝑡ℎ 𝑎 𝑠𝑙𝑜𝑝𝑒 𝑜𝑓 − 4
Point-Slope Form
The point-slope form of the equation of a line is
𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1 ),
where (𝑥1 , 𝑦1 ) are the coordinates of a point on
the line and 𝑚 is the slope of the line.
Point-Slope Form
Option 1: Given the slope and a
point on the line.
𝑚 = −4, 𝑡ℎ𝑎𝑡 𝑝𝑎𝑠𝑠𝑒𝑠 𝑡ℎ𝑟𝑜𝑢𝑔ℎ (6, −2)
Point-Slope Form
Option 2: Given two points on the
line.
𝑝𝑎𝑠𝑠𝑒𝑠 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 2, 3 𝑎𝑛𝑑 (−1, 5)
Try It On Your Own
Write an equation of the line.
1. 𝑝𝑎𝑠𝑠𝑒𝑠 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 2, 3 𝑤𝑖𝑡ℎ 𝑎 𝑠𝑙𝑜𝑝𝑒 𝑜𝑓
2. 𝑝𝑎𝑠𝑠𝑒𝑠 𝑡ℎ𝑟𝑜𝑢𝑔ℎ −2, −1 𝑎𝑛𝑑 (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. 𝒚 =
𝟏
𝒙
𝟐
−
𝟑
𝟐
B. 𝒚 = −𝟐𝒙 + 𝟑
C. 𝒚 =
𝟏
𝒙
𝟐
+𝟖
D. 𝒚 = 𝟐𝒙 + 𝟏𝟏
Parallel Lines
How do you know if two lines are parallel?
Their SLOPES are the SAME!
𝑦 = 3𝑥 − 1 and 𝑦 = 3𝑥 + 13
𝑦=
1
𝑥
2
and 𝑦 =
1
𝑥
2
+1
Example
Write an equation of a line that passes through
𝟏
(12, 0) and is parallel to 𝒚 = − 𝒙 − 𝟑.
𝟐
Write an equation of a line that passes through (0, 9)
𝟐
and is parallel to 𝒚 = 𝒙 − 𝟏𝟎.
𝟑
Perpendicular Lines
How do you know if two lines are perpendicular?
Their SLOPES are the NEGATIVE RECIPROCALS!
𝑦 = 3𝑥 − 1 and 𝑦 =
𝑦 = −2𝑥 and 𝑦 =
1
− 𝑥
3
1
𝑥
2
+ 13
+1
Example
Write an equation of a line that passes through
𝟐
(5, -6) and is perpendicular to 𝒚 = − 𝒙 + 𝟕.
𝟑
Write an equation of a line that passes through
(6, -1) and is parallel to 𝒚 = 𝟑𝒙 − 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