 # TODAY IN ALGEBRA… Warm up: 5.2 Review-Writing an equation of a line given two points Learning Goal: 5.3 Writing a linear equation in Point-Slope form.

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TODAY IN ALGEBRA… Warm up: 5.2 Review-Writing an equation of a line given two points Learning Goal: 5.3 Writing a linear equation in Point-Slope form Independent Practice

WARM UP: Write an equation for the linear function 𝑓 with the values 𝑓 −2 =10 and 𝑓 4 =−2
Rewrite function values as coordinate pairs (points): 2. Calculate slope: 𝑚= 𝑚= −12 6 Calculate the y-intercept: 𝑦=𝑚𝑥+𝑏 −2=−2 4 +𝑏 −2=−8+𝑏 𝟔=𝒃 −𝟐, 𝟏𝟎 , (𝟒, −𝟐) 𝑥 𝑦 −2−10 REMEMBER: 𝒇(𝒙)=𝒎𝒙+𝒃 4−(−2) =−𝟐 𝑚→ 𝑠𝑙𝑜𝑝𝑒: 𝑦−𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡: −2 6 𝑏→ 𝑓(𝑥)= 𝑥+ −2 6

New…POINT-SLOPE FORM:
5.3 WRITING LINEAR EQUATIONS IN POINT-SLOPE FORM We learned… SLOPE-INTERCEPT FORM: New…POINT-SLOPE FORM: 𝑦− 𝑦 1 =𝑚(𝑥− 𝑥 1 ) 𝑦=𝑚𝑥+𝑏 𝑠𝑙𝑜𝑝𝑒= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 𝑝𝑜𝑖𝑛𝑡: ( 𝑥 1 , 𝑦 1 ) 𝑠𝑙𝑜𝑝𝑒= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 𝑦−𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡: (0, 𝑏) 𝑠𝑙𝑜𝑝𝑒= 1 3 𝑔𝑖𝑣𝑒𝑛 𝑝𝑜𝑖𝑛𝑡:(4, 2) 𝑦− = (𝑥− ) 1 3 2 4

𝑦− = 𝑥− 𝑦+3=2(𝑥−4) 𝑦− = 𝑥− 𝑦−4=−2(𝑥+1) −3 2 4 4 −2 −1
5.3 WRITING LINEAR EQUATIONS IN POINT-SLOPE FORM PRACTICE: Write an equation of the line in point-slope form given a point and slope. REMEMBER: 𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 ) 1. 𝑠𝑙𝑜𝑝𝑒: 𝑠𝑙𝑜𝑝𝑒:−2 𝑝𝑜𝑖𝑛𝑡:(4, −3) 𝑝𝑜𝑖𝑛𝑡:(−1, 4) 𝑦− = 𝑥− 𝑦+3=2(𝑥−4) −3 2 4 𝑦− = 𝑥− 𝑦−4=−2(𝑥+1) 4 −2 −1

On a separate piece of paper try the following problems:
PRACTICE: (10 MINUTES) On a separate piece of paper try the following problems: Pg. 305: 3-11

1. 𝑦+3=2 𝑥−4 𝑦+3=2𝑥−8 − 3 − 3 𝒚=𝟐𝒙−𝟏𝟏 𝑠𝑙𝑜𝑝𝑒: 𝑦−𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡:
5.3Changing POINT-SLOPE FORM to SLOPE-INTERCEPT FORM Rewrite the equation into slope-intercept form. SOLVE FOR Y! 1. 𝑦+3=2 𝑥−4 𝑦+3=2𝑥−8 − − 3 𝒚=𝟐𝒙−𝟏𝟏 𝑠𝑙𝑜𝑝𝑒: 𝑦−𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡: 2. 𝑦−4=−2 𝑥+1 𝑦−4=−2𝑥−2 𝒚=−𝟐𝒙+𝟐 𝑠𝑙𝑜𝑝𝑒: 𝑦−𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡: 2 −2 −11 2

𝑦+2= 2 3 (𝑥−3) 2 3 𝑠𝑙𝑜𝑝𝑒: 𝑝𝑜𝑖𝑛𝑡: (3, −2)
5.3 Graphing equations in POINT-SLOPE FORM **Points are always opposite the sign!!! Graph the equation: 𝑝𝑜𝑖𝑛𝑡:( 𝑥 1 , 𝑦 1 ) REMEMBER: 𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 ) 𝑦+2= 2 3 (𝑥−3) 𝑠𝑙𝑜𝑝𝑒= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 3 2 𝑡𝑜 𝑔𝑒𝑡 𝑡𝑜 𝑛𝑒𝑥𝑡 𝑝𝑜𝑖𝑛𝑡→ 2 3 𝑠𝑙𝑜𝑝𝑒: 𝑝𝑜𝑖𝑛𝑡: (3, −2) 𝑠𝑡𝑎𝑟𝑡→

𝑦−2= 1 2 (𝑥+2) 1 2 𝑠𝑙𝑜𝑝𝑒: 𝑝𝑜𝑖𝑛𝑡: (−2, 2)
5.3 Graphing equations in POINT-SLOPE FORM **Points are always opposite the sign!!! PRACTICE: Graph the equation: 𝑝𝑜𝑖𝑛𝑡:( 𝑥 1 , 𝑦 1 ) REMEMBER: 𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 ) 𝑦−2= 1 2 (𝑥+2) 𝑠𝑙𝑜𝑝𝑒= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 2 𝑡𝑜 𝑔𝑒𝑡 𝑡𝑜 𝑛𝑒𝑥𝑡 𝑝𝑜𝑖𝑛𝑡→ 1 2 1 𝑠𝑙𝑜𝑝𝑒: 𝑝𝑜𝑖𝑛𝑡: (−2, 2) 𝑠𝑡𝑎𝑟𝑡→

On the same piece of paper try the following problems:
PRACTICE: (15 MINUTES) On the same piece of paper try the following problems: Pg. 306: 14-19

5.3 Writing equations in POINT-SLOPE FORM given a graph
Write an equation in point-slope form of the line shown. REMEMBER: 𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 ) 1. Find slope: 𝑠𝑙𝑜𝑝𝑒= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 𝑚=−1 Choose one point: *doesn’t matter which one* (1, 1) 3. Plug into point-slope form. (−1, 3) = −2 2 −2 (1, 1) 2 𝑦− = 𝑥− 𝑦−1=−(𝑥−1) 1 −1 1

5.3 Writing equations in POINT-SLOPE FORM given points
Write an equation in point-slope form given the two points. REMEMBER: 𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 ) 𝟐, 𝟑 , (𝟒, 𝟒) 1. Find slope: 𝑚= 𝑚= 1 2 Choose one point. *doesn’t matter which one* 3. Plug into point-slope form. 4−3 1 2 4−2 𝑦− = 𝑥− 𝑂𝑅 3 2 (𝟐, 𝟑)  1 2 4 4 (𝟒, 𝟒)

HOMEWORK #4: Pg. 305: 3-30 all If finished, work on other assignments:
HW #1: Pg. 286: 3-23 all HW #2: Pg. 286: all HW #3: Pg. 296: 3-7, 11-14, 22-25

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