1. Homework Log Wed 10/28 Lesson 3 – 1 Learning Objective:
To graph linear equations & find slope
Hw: #301 Pg. 168 #1 – 29 odd

2. 10/28/15 Lesson 3 – 1 Linear Equations Day 1
Advanced Math/Trig
Ch 3 Quiz on
Thursday 11/12/15
Ch 3 TEST on
Monday 11/16/15

3. Learning Objective To graph linear equations To find x & y intercepts
To find slope
To find midpoint

4. Linear Equation: Ax + By = C
Graph by finding: x – intercept y - intercept (x , 0) (0 , y) let y = 0 let x = 0 Solve for x Solve for y
Slope Intercept Form: y = mx + b
Graph y-int (0, b)
Use slope (m) to find another point
𝑚= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛

5. Graph & Find x & y intercepts
Let x=0: 2(0) +3y = 6
3y = 6
y = 2
(0, 2) y x
Y-int
(0, 2)
Let y=0: 2x +3(0) = 6
2x = 6
x = 3
(3, 0)
(3, 0)
X-int
Graph intercepts and connect the dots

6. Graph & Find x & y intercepts
b = 2  (0, 2)
 y-int
𝑚=− 5 2
y = mx + b
𝑢𝑝 𝑙𝑒𝑓𝑡 or 𝑑𝑜𝑤𝑛 𝑟𝑖𝑔ℎ𝑡 y x
Find x-int: Let y = 0
0 = − 5 2 𝑥+2
(2) 0 =( − 5 2 𝑥+2 )(2)
0 = –5x + 4
5x = 4
x = ( 4 5 , 0)
(0, 2)
(2, –3)

7. Graph & Find x & y intercepts
3. Graph 3y = – 6x x & y intercept both at (0, 0) Get into y = mx + b 3y = – 6x y = – 2x m = − 2 1 𝑢𝑝 𝑙𝑒𝑓𝑡 y – int (0, 0)

8. Two Special Cases x = -3 (no y) y = 2 (no x) Undefined Zero
I only see an “x”
It goes thru x-axis
x = (no y)
I only see
a “y”
It goes thru y-axis
y = (no x) y x y x
Undefined
Zero
Vertical line thru
(-3, 0)
Undefined Slope
Horizontal line thru
(0, 2)
Zero Slope

9. Graphing vertical lines
4. Graph 3x = 12 It ONLY has x, so solve for x. 3x = 12 x = 4 x ALWAYS equals 4

10. 5. Graph a line with slope of 0 and goes through (-3, 4) Slope = 0 Horizontal Line at y = 4

11. Slope Formula 𝑆𝑙𝑜𝑝𝑒=𝑚= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1
Given 2 points: (x1, y1) and (x2, y2)
The slope of the line through the points is
𝑆𝑙𝑜𝑝𝑒=𝑚= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1

12. Find Slope
6. Find slope (3, -5) (7, -2) (x1, y1) (x2, y2) 𝑚= 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 = −2−(−5) 7−3 = −2+5 4 = 3 4

13. Special Cases
m= 0 # = 0 m= # 0 = undefined
0 𝐾
𝑁 0 way!

14. Find Slope 𝑚= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏
7. (3, 1) & (– 4, 1) 𝑚= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 = 𝟏−𝟏 −𝟒−𝟑 = 𝟎 −𝟕 =𝟎 horizontal line! At y = 1

15. Find Slope 𝑚= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏
8. (7, 3) & (7, 1) 𝑚= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 = 𝟏−𝟑 𝟕−𝟕 = −𝟐 𝟎 =𝒖𝒏𝒅𝒆𝒇𝒊𝒏𝒆𝒅 vertical line! at x = 7
CANNOT DIVIDE BY ZERO!!

16. Midpoint Formula

17. Find Midpoint 9. (4, 0) & (– 10, 3) (x1, y1) (x2, y2)
= 4+(−10) 2 ,
= −3, 3 2

18. Find Midpoint 10. (a, b) & (– a, b) (x1, y1) (x2, y2)
= 𝑎+(−𝑎) 2 , 𝑏+𝑏 2
= , 2𝑏 2
= 0, 𝑏

19. Find Midpoint 10𝜋 4 2 = 10𝜋 4 ÷2 = 10𝜋 4 ∙ 1 2 = 10𝜋 8 = 5𝜋 4
11. ( 𝜋 4 , 0) & ( 9𝜋 4 , 0)
(x1, y1) (x2, y2)
Midpoint = 𝑥 1 + 𝑥 2 2 , 𝑦 1 + 𝑦 2 2
= 𝜋 4 + 9𝜋 4 2 ,
= 10𝜋 4 2 , 0 2
= 5𝜋 4 ,0
10𝜋
= 10𝜋 4 ÷2
= 10𝜋 4 ∙ 1 2
= 10𝜋 8
= 5𝜋 4

20. Ticket Out the Door
None today!

21. Homework
#301 Pg. 168 #1 – 29 odd