Section 1.1 Slopes and Equations of Lines

Slides:

Advertisements

Similar presentations

A3 2.4 Parallel and Perpendicular Lines, Avg. rate of change

Advertisements

Parallel & Perpendicular Lines

5.7 Parallel and Perpendicular Lines

Chapter 3 Introduction to Graphing and Equations of Lines

2.5 The Point-Slope Form of the Equation of a Line.

Geometry Section 3.6 “Slope of Parallel and Perpendicular lines”

Warm Up Solve each equation for y. 1. y – 6x = 92. 4x – 2y = 8 2.9A Parallel and Perpendicular Lines.

2.5 Linear Equations. Graphing using table Graphing using slope and y-intercept (section 2.4) Graphing using x-intercept and y-intercept (section 2.5)

Equations of lines.

Equations of Lines; Building Linear Functions January 22, 2007.

2.3 Linear Functions.

Rates of Change (Slope)

The slope of a line. We define run to be the distance we move to the right and rise to be the corresponding distance that the line rises (or falls). The.

1.3 Linear Equations in Two Variables Objectives: Write a linear equation in two variables given sufficient information. Write an equation for a line.

Copyright © Cengage Learning. All rights reserved. 1.1 Lines in the Plane.

Sullivan Algebra and Trigonometry: Section 2.3 Objectives Calculate and Interpret the Slope of a Line Graph Lines Given a Point and the Slope Use the Point-Slope.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

Slopes of Equations and Lines Honors Geometry Chapter 2 Nancy Powell, 2007.

Goal: Write a linear equation..  1. Given the equation of the line 2x – 5y = 15, solve the equation for y and identify the slope of the line.  2. What.

Day Problems Graph each equation.

Slopes and Parallel Lines Goals: To find slopes of lines To identify parallel lines To write equations of parallel lines.

1. A line passes through (3, 5) and (6, 14). What is the equation of the line in point-slope form? 2. Write an equation of a line parallel to -3x + y =

HPC 1.6 Notes Learning Targets: - Interpret the slope of a line - Write equations in slope-intercept form - Write equations in point-slope form.

Section 2.4 Notes: Writing Linear Equations. Example 1: Write an equation in slope-intercept form for the line.

Linear Models & Rates of Change (Precalculus Review 2) September 9th, 2015.

Point-Slope Formula Writing an Equation of a line Using the Point-Slope Formula.

3-7 Equations of Lines in the Coordinate Plane

Geometry: Parallel and Perpendicular Lines

Writing Equations of a Line. Various Forms of an Equation of a Line. Slope-Intercept Form.

Lines. Slope Measure of units the line rises for each unit of horizontal change - symbol (m) m = Δy = y 2 – y 1 Δx x 2 – x 1 if x 2 = x 1 then m is undefined.

Slopes of Parallel and Perpendicular Lines (3.6) Objective: To relate slope of parallel and perpendicular lines, and to write equations of parallel and.

Section 2.5 Other Equations of Lines  Point-Slope Form (y – y 1 )=m(x – x 1 )  Special pairs of lines: Parallel Lines m 1 = m 2 Perpendicular lines m.

Warm Up Find the value of m B Writing the Equation of the Line.

 Parallel Lines = Lines in the same plane that never intersect.  Review:  Slope-Intercept form: y = mx+b.

2.4 Essential Questions What is the point-slope form?

For the line that passes through points (-4, 3) and (-2, 4).

Slopes and Equations of Lines Advanced Geometry Parallel and Perpendicular Lines Lesson 2.

Linear Equations in Two Variables

What are the characteristics of Lines in the Plane? Section P4 (new text)

Are You Smarter Than a 5 th Grader? 1,000,000 5th Grade 5th Grade Equations 5th Grade 5th Grade Equations 5th Grade 5th Grade Equations 4th Grade 4th.

Warm Up Given: (3, -5) and (-2, 1) on a line. Find each of the following: 1.Slope of the line 2.Point-Slope equation of the line 3.Slope-Intercept equation.

Write an equation of a line by using the slope and a point on the line.

Functions and Their Graphs 1.1 Lines in the Plane.

Copyright 2013, 2009, 2005, 2002 Pearson, Education, Inc.

Graphing Test Review Algebra.

2.4 Lines. Slope Find the slope of the line passing through the given points.

Notes Over 2.1 Graphing a Linear Equation Graph the equation.

Notes A7 Review of Linear Functions. Linear Functions Slope – Ex. Given the points (-4, 7) and (-2, -5) find the slope. Rate of Change m.

Point-Slope Form The line with slope m passing through the point (x1, y1) has an equation the point –slope form of the equation of a line.

Algebra 1 Notes Lesson 5-6: Parallel and Perpendicular Lines.

Geometry Section 3.7 cont. “Writing Equations of Lines”

5-6 PARALLEL AND PERPENDICULAR LINES. Graph and on the same coordinate plane. Parallel Lines: lines in the same plane that never intersect Non-vertical.

1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-1 Graphs and Functions Chapter 3.

Lesson 3-7: Parallel & Perpendicular Lines Objectives Students will: Use equations to determine if two lines are parallel or perpendicular Write an equation.

Equations of Lines in the Coordinate Plane and Slopes of Parallel and Perpendicular Lines Objective: Students will find the slopes of lines and.

Write Equations of Parallel and Perpendicular Lines

I can determine when lines are parallel and write equations of parallel lines.

3-8 Slopes of Parallel and Perpendicular Lines. Slopes of Parallel Lines If two nonvertical lines are parallel, then their slopes are equal If the slopes.

Section 6.5: Parallel and Perpendicular Lines Objectives: Determine whether lines are parallel Determine whether lines are perpendicular Write equations.

1)-1 – 4 2) 0 – (-2) 4 – ( -3) -1 – (-2) 3)3 – 4 4) 2 – (-2) – 6.

Slopes of Parallel and Perpendicular Lines. Different Forms of a Linear Equation  Standard Form  Slope-Intercept Form  Point-Slope Form  Standard.

MTH 100 The Slope of a Line Linear Equations In Two Variables.

Section 3-7 Equations of Lines in the Coordinate Plane Michael Schuetz.

P.2 Linear Models & Rates of Change 1.Find the slope of a line passing thru 2 points. 2.Write the equation of a line with a given point and slope. 3.Interpret.

Writing Equations of Parallel Lines (IN REVIEW) You can use the slope m of a nonvertical line to write an equation of the line in slope-intercept form.

Slope and Equations of Lines. Reviewing types of slope Remember, there are four types of slope: PositiveNegative No slope Undefined slope.

1.3 Linear Equations in Two Variables. I. Using Slope.

LESSON 20 PREREQ B: Writing the Equation of a Line.

Warm Up! – Graph the line that satisfies each condition

2.5 Linear Equations.

Presentation transcript:

Section 1.1 Slopes and Equations of Lines

Slope of a line If a line passes through two points (x1,y1) and (x2,y2), then its slope is given by The slope of a horizontal line is 0 The slope of a vertical line is undefined

Slope-Intercept form of a line If a line has slope m and y-intercept (0,b), then the equation of the line is given by

Example Graph Solution: The y-intercept is (0, 2).

Point-Slope form of a line If a line has slope m and passes through a point (x1,y1), then the equation of the line is given by

Example Find the equation of the line containing the points (2, 7) and (1, 8). Solution: First determine the slope: Using the point-slope equation,

Horizontal and vertical lines Horizontal line has equation of the form Vertical line has equation of the form

General Form of a Line Examples: 2x + y = 10 x – 5 = 1 3y – 9 = 0

Parallel Lines Vertical lines are parallel. Nonvertical lines are parallel if and only if they have the same slope and different y-intercepts. y = 3x + 2 y = 3x  4

Perpendicular Lines Two lines with slopes m1 and m2 are perpendicular if and only if the product of their slopes is 1: m1m2 = 1. Lines are also perpendicular if one is vertical (x = a) and the other is horizontal (y = b). y = 3x  4

Examples Determine whether each of the following pairs of lines is parallel, perpendicular, or neither. a) y  4x =  3, 4y  8 =  x (perpendicular) b) 2x + 3y = 4, 3x + 2y = 8 (neither) c) 2y = 4x + 12, y  8 = 2x (parallel)

Example Write an equation of the line containing the point (1,  2) and is (a) parallel to the line 3y + 4 = 18x. (b) perpendicular to the line 3y + 4 = 18x. Solution: Solve the equation for y: So, its slope is 6.

Example continued The line parallel to the given line will have the same slope, which is 6.

Example continued (b) For a line perpendicular, its slope will be m =