1. Warm – up #3
1. Write an equation of a line with slope 4 and y-intercept at (0, -3) 2. Write 12 – y = 2x – 5 in slope- intercept form. What are the slope and y-intercept? 3. Find perpendicular slope to (-2, 3) & (4, -5)

2. Warm – up #3 Solutions
1. y = 4x – y = 2x y = 2x – y = -2x + 17 slope = -2 y-int: (0, 17)

3. Warm – up #3 Solutions
3. (-2, 3) & (4, -5) (x1, y1) & (x2, y2) 𝑚= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 = −𝟓−𝟑 𝟒−(−𝟐) = −𝟖 𝟔 =− 𝟒 𝟑 Perpendicular Slope = 𝟑 𝟒

4. Homework Log Thurs 9/24 Lesson 2 – 4 Learning Objective:
To write an eq’n of a line given slope & a point
Hw: Pg. 86 # 11 – 25 odd, 32 – 35, *9, *45 CC

5. Homework Log Fri 9/25 Lesson Rev Learning Objective:
To remember everything from 2.1 – 2.4
Hw: 2.1 – 2.4 Review WS

6. 9/24/15 Lesson 2-4 More About Linear Equations Day 1
Algebra II

7. Learning Objective
To write an equation of a line given its slope and a point on the line

8. Slope-Intercept Form 𝑦=𝑚𝑥+𝑏
Use to write an equation of a line when given the slope m and the
y-intercept b

9. Point-Slope Form 𝑦− 𝑦 1 =𝑚 𝑥− 𝑥 1
Use to write an equation of a line when given a point (x1, y1) and slope m
*May need to find slope if given two points, then use point-slope form to write the linear equation

10. Standard Form
𝐴𝑥+𝐵𝑦=𝐶
A, B, C are integers (no fractions)

11. Parallel Lines – have the same slope
Perpendicular Lines – have opposite reciprocal slopes

12. Given a point & the slope
1. A line passes through (-5, 2) with slope What is the equation of the line in point-slope form? 𝑦− 𝑦 1 =𝑚 𝑥− 𝑥 1 𝑦−2= 3 5 𝑥− −5 𝑦−2= 3 5 𝑥+5

13. Given a point & the slope
2. A line passes through (7, -1) with slope -3. What is the equation of the line in point-slope form? 𝑦− 𝑦 1 =𝑚 𝑥− 𝑥 1 𝑦− −1 =−3 𝑥−7 𝑦+1=−3 𝑥−7

14. Given two points
3. A line passes through (3, 2) and (5, 8). What is the equation of the line in point-slope form? * Find Slope 𝑚= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 = 𝟖−𝟐 𝟓−𝟑 = 𝟔 𝟐 =𝟑 ** Use the slope and EITHER point. 𝑦− 𝑦 1 =𝑚 𝑥− 𝑥 1 y – 2 = 3(x – 3) or y – 8 = 3(x – 5)

15. Given two points
4. A line passes through (-5, 0) and (0, 4). What is the equation of the line in point-slope form? * Find Slope 𝑚= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 = 𝟎−𝟒 −𝟓−𝟎 = −𝟒 −𝟓 = 𝟒 𝟓 ** Use the slope and EITHER point. 𝑦− 𝑦 1 =𝑚 𝑥− 𝑥 1 y – 0 = 𝟒 𝟓 (x –(-5)) or y – 4 = 𝟒 𝟓 (x – 0) y = 𝟒 𝟓 (x +5) or y – 4 = 𝟒 𝟓 x

16. Given two points
5. Using #4, what is the equation of the line in slope-intercept form? * We know the slope is 𝟒 𝟓 ** We know the y-intercept is (0, 4) y = mx + b y = 𝟒 𝟓 x + 4

17. Given two points
6. Using #4 & #5, what is the equation of the line in standard form? *We know the slope-intercept form is y = 𝟒 𝟓 x + 4 (5) y =( 𝟒 𝟓 x + 4)(5) 5y = 4x x -4x -4x + 5y = 20 or 4x – 5y = -20

18. Parallel Lines
7. What is the equation of a line parallel to y = 6x – 2 that goes through (1, -3) in slope-intercept form? *Parallel lines have same slope, so m = 6 y – (-3) = 6(x – 1) y + 3 = 6x – y = 6x - 9

19. Perpendicular Lines
8. What is the equation of a line perpendicular to y = -4x + 1 that goes through (8, 5) in slope-intercept form? *Perpendicular lines have opposite reciprocal slopes, so m = 1 4 y – 5 = 1 4 (x – 8) y - 5 = 1 4 x y = 1 4 x +3

20. Parallel Lines
9. What is the equation of a line parallel to 4x + 2y = 7 that goes through (4, -2) in standard form? *Find slope of original line 4x + 2y = 7 -4x -4x 2y = -4x y = -2x Slope = -2

21. Parallel Lines
9. Slope = -2, Goes through (4, -2) in standard form? y – (-2) = -2(x – 4) y + 2 = -2x y = -2x x +2x 2x + y = 6
Start with point slope form
Slope-intercept form!
End with standard form!

22. Summary
If you have a point and the slope, Then you can find point-slope form y + 2 = -2(x – 4) Then you can find slope-intercept form y = -2x + 6 Then you can find standard form 2x + y = 6

23. Perpendicular Lines
10. Using #9, write an equation of a line perpendicular to 4x + 2y = 7 in standard form. Slope = -2 Goes through (4, -2) perpendicular slope = 1 2 y – (-2) = 1 2 (x – 4) y + 2 = 1 2 x y = 1 2 x - 4 (2)y = ( 1 2 x – 4)(2) 2y = x – 8 -x -x -x + 2y = -8 or x – 2y = 8

24. Perpendicular Lines
11. What is the equation of a line perpendicular to -2x + 3y = - 3 and goes through (0, 6) in slope- intercept form? -2x + 3y = x +2x 3y = 2x – y= 2 3 𝑥−1
Perpendicular slope = − 3 2
y=− 3 2 𝑥+6

25. Find x & y intercepts
12. – 4x + 6y = 12 x-intercept (y = 0) – 4x + 6(0) = 12 – 4x = 12 x = –3 (–3, 0) y-intercept (x = 0) –4(0) + 6y = 12 3y = 12 y = 2 (0, 2)

26. Ticket Out the Door Each interval is one unit
Write an equation for the line shown.
(Any form)
*Hint: what do
You know from
The graph?
Which form of equation can you use with the info?

27. Assignment: Pg. 86 # 11 – 25 odd, 32 – 35, *9, *45 CC