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

1. y = 4x - 3

2. 12 – y = 2x - 5 -12 -12

-y = 2x – 17-1 -1 -1y = -2x + 17

slope = -2 y-int: (0, 17)

Warm – up #3 Solutions

3. (-2, 3) & (4, -5) (x1, y1) & (x2, y2)

Perpendicular Slope =

Warm – up #3 Solutions

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 1Algebra II

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

Learning Objective

Slope-Intercept Form

Use to write an equation of a line when given the slope m and the y-intercept b

Point-Slope Form

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

A, B, C are integers (no fractions)

Parallel Lines – have the same slope

Perpendicular Lines – have opposite reciprocal slopes

1. A line passes through (-5, 2) with slope . What is the equation of the line in point-slope form?

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?

Given a point & the slope

3. A line passes through (3, 2) and (5, 8). What is the equation of the line in point-slope form?* Find Slope

** Use the slope and EITHER point.

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

** Use the slope and EITHER point.

y – 0 = (x –(-5)) or y – 4 = (x – 0)y = (x +5) or y – 4 = x

Given two points

5. Using #4, what is the equation of the line in slope-intercept form?* We know the slope is ** We know the y-intercept is (0, 4)

y = mx + by = 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 = x + 4

(5) y =( x + 4)(5)5y = 4x + 20-4x -4x

-4x + 5y = 20 or 4x – 5y = -20

Given two points

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 = 6y – (-3) = 6(x – 1)y + 3 = 6x – 6 -3 -3

y = 6x - 9

Parallel 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 =

y – 5 = (x – 8)y - 5 = x - 2 + 5 + 5

y = x +3

Perpendicular 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 2y = -2x + Slope = -2

Parallel Lines

9. Slope = -2, Goes through (4, -2) in standard form?

y – (-2) = -2(x – 4)y + 2 = -2x + 8 -2 - 2y = -2x + 6

+2x +2x2x + y = 6

Parallel Lines

Slope-intercept form!

Start with point slope form

End with standard form!

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

Summary

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 = y – (-2) = (x – 4) y + 2 = x - 2

-2 -2y = x - 4

(2)y = (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 +2x3y = 2x – 33 3 3

Perpendicular Lines

Perpendicular slope =

y=−32𝑥+6

12. – 4x + 6y = 12x-intercept (y = 0)

– 4x + 6(0) = 12– 4x = 12 x = –3(–3, 0)

y-intercept (x = 0) –4(0) + 6y = 123y = 12y = 2(0, 2)

Find x & y intercepts

Each interval is one unitWrite an equation for the line shown.

(Any form)*Hint: what do You know fromThe graph?

Which form of equation can you use with the info?

Ticket Out the Door

Assignment:

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