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)

Warm – up #3 Solutions 1. y = 4x - 3 2. 12 – y = 2x - 5 -12 -12 -y = 2x – 17 -1 -1 -1 y = -2x + 17 slope = -2 y-int: (0, 17)

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

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

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

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

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

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

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

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

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

Given a point & the slope 1. A line passes through (-5, 2) with slope 3 5 . 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

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

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)

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

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

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 + 20 -4x -4x -4x + 5y = 20 or 4x – 5y = -20

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 – 6 -3 -3 y = 6x - 9

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 - 2 + 5 + 5 y = 1 4 x +3

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 + 7 2 2 2 y = -2x + 7 2 Slope = -2

Parallel Lines 9. Slope = -2, Goes through (4, -2) in standard form? y – (-2) = -2(x – 4) y + 2 = -2x + 8 -2 - 2 y = -2x + 6 +2x +2x 2x + y = 6 Start with point slope form Slope-intercept form! End with standard form!

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

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 - 2 -2 -2 y = 1 2 x - 4 (2)y = ( 1 2 x – 4)(2) 2y = x – 8 -x -x -x + 2y = -8 or x – 2y = 8

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 = - 3 +2x +2x 3y = 2x – 3 3 3 3 y= 2 3 𝑥−1 Perpendicular slope = − 3 2 y=− 3 2 𝑥+6

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)

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?

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