Transcript TODAY IN ALGEBRA…  Warm up: Calculating Slope  Learning Goal: 5.1b You will write equations of lines in slope intercept form given two.

TODAY IN ALGEBRA…
 Warm up: Calculating Slope
 Learning Goal: 5.1b You will write
equations of lines in slope intercept
form given two points
 Independent Practice
WARM UP: Find the slopes of the line that passes
through the points:
1. 2, −1 , (4, 0)
𝑚=
𝑚=
𝑚=
2. −1, −3 , (1, 5) 𝑚 =
𝑚=
𝑚=
𝑦2 −𝑦1
𝑥2 −𝑥1
0−2
4 − (−1)
−2
𝟐
=−
5
𝟓
𝑦2 −𝑦1
𝑥2 −𝑥1
5 − (−3)
1 − (−1)
8
=𝟒
2
5.1 WRITING LINEAR EQUATIONS IN SLOPE-INTERCEPT FORM
Given two points find the y-intercept:
0, 2 , (4, 4)
𝑏=2
PRACTICE: Given two points find the
y-intercept.
1. 2, −1 , (0, 4)
𝑏=4
2. 0, −3 , (1, 5)
𝑏 = −3
y-intercept
(0, 2)
REMEMBER:
𝒚 = 𝒎𝒙 + 𝒃
5.1 WRITING LINEAR EQUATIONS IN SLOPE-INTERCEPT FORM
GIVEN TWO POINTS!
Write an equation of the line that passes through the given
points:
REMEMBER:
𝟎, −𝟓 , (𝟑, −𝟏)
𝒚 = 𝒎𝒙 + 𝒃
1. Calculate slope:
𝑦2 −𝑦1
4
𝑚=
𝑚 → 𝑠𝑙𝑜𝑝𝑒: 3
𝑥2 −𝑥1
𝑏 → 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡:−5
−1 − (−5)
𝑚=
4
𝟒
𝟑
3−0
𝑚=
2. Find the y-intercept (𝟎, 𝒃):
(0, −5)
𝑏 = −5
𝑦=
𝑦=
3
𝑥 +−5
4
𝑥
3
−5
5.1 WRITING LINEAR EQUATIONS IN SLOPE-INTERCEPT FORM
GIVEN TWO POINTS!
PRACTICE: Write an equation of the line that passes through
the given points:
REMEMBER:
𝟎, 𝟏 , (𝟒, −𝟏)
𝒚 = 𝒎𝒙 + 𝒃
1. Calculate slope:
𝑦2 −𝑦1
1
𝑚=
𝑚 → 𝑠𝑙𝑜𝑝𝑒: − 2
𝑥2 −𝑥1
𝑏 → 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡: 1
−1 − 1
𝑚=
4
4−0
−2
𝟏
=−
𝟐
4
𝑚=
2. Find the y-intercept (𝟎, 𝒃):
(0, 1)
𝑏=1
𝑦=
3
𝑥+1
5.1 WRITING LINEAR EQUATIONS IN SLOPE-INTERCEPT FORM
Rewrite the function values as
coordinate pairs:
𝑥
𝑦
𝑥
𝑦
𝑓 0 = 3, 𝑓 −4 = 11
(0, 3)
(−4, 11)
REMEMBER:
FUNCTION NOTATION
𝒇(𝒙) = 𝒎𝒙 + 𝒃
𝒚=𝒇 𝒙
𝒙=𝒙
PRACTICE: Rewrite the function values as coordinate pairs:
𝑥
𝑦
𝑥
𝑦
1. 𝑓 −4 = 6, 𝑓 0 = −2
(−4, 6)
(0, −2)
𝑥
𝑦
𝑥
𝑦
2. 𝑓 10 = 4, 𝑓 −8 = 2
(10, 4)
(−8, 2)
5.1 WRITING LINEAR EQUATIONS IN SLOPE-INTERCEPT FORM
GIVEN TWO POINTS IN FUNCTION NOTATION!
Write an equation for the linear function 𝑓 with the values
𝑓 0 = 5 and 𝑓 4 = 17
REMEMBER:
𝟎, 𝟓 , (𝟒, 𝟏𝟕)
𝒇(𝒙) = 𝒎𝒙 + 𝒃
1. Calculate slope:
𝑦2 −𝑦1
12
𝑚=
𝑚 → 𝑠𝑙𝑜𝑝𝑒: 5
𝑥2 −𝑥1
𝑏 → 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡: 5
17 − 5
𝑚=
12
𝟏𝟐
𝟓
5−0
𝑚=
2. Find the y-intercept (𝟎, 𝒃):
(0, 5)
𝑏=5
𝑓(𝑥) =
5
𝑥 +5
5.1 WRITING LINEAR EQUATIONS IN SLOPE-INTERCEPT FORM
GIVEN TWO POINTS IN FUNCTION NOTATION!
PRACTICE: Write an equation for the linear function 𝑓 with
the values 𝑓 0 = 3 and 𝑓 −4 = 11
REMEMBER:
𝟎, 𝟑 , (−𝟒, 𝟏𝟏)
𝒇(𝒙) = 𝒎𝒙 + 𝒃
1. Calculate slope:
𝑦2 −𝑦1
𝑚=
𝑚 → 𝑠𝑙𝑜𝑝𝑒: −2
𝑥2 −𝑥1
𝑏 → 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡: 3
11 − 3
𝑚=
−4 − 0
𝑓(𝑥)
=
−2 𝑥 + 3
8
𝑚 = = −𝟐
−4
2. Find the y-intercept (𝟎, 𝒃):
(0, 5)
𝑏=3
HOMEWORK #2:
Pg. 286: 24-38 all
If finished, work on other assignments:
HW #1: Pg. 286: 3-23 all