1. 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

2. 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

3. 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

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

5. 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

6. 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

7. 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→

8. 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→

9. 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

10. 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

11. 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)

12. 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