Review of lines Section 2-A. Slope (m) of a line Let P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ) be points on a nonvertical line, L. The slope of L is.

Slides:



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

Parallel & Perpendicular Lines
Perpendicular Lines. ┴ Perpendicular lines are lines that intersect in a right angle. ┴ The slopes of perpendicular lines are negative reciprocals of.
7.8 Parallel and Perpendicular Lines Standard 8.0: Understand the concepts of parallel and perpendicular lines and how their slopes are related.
Lesson 6.5 Parallel and Perpendicular Lines
5.6 Parallel and Perpendicular Lines
5.7 Parallel and Perpendicular Lines
Chapter 3 Introduction to Graphing and Equations of Lines
Writing equations given slope and point
Copyright © Cengage Learning. All rights reserved.
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)
Slope-Intercept and Point-Slope Forms of a Linear Equation
Section 2.3 Linear Functions: Slope, Graphs & Models  Slope  Slope-Intercept Form y = mx + b  Graphing Lines using m and b  Graphs for Applications.
Equations of lines.
2.2 Slope and Rate of Change Algebra 2 Mrs. Spitz Fall 2009.
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.
1.2 Linear Equations in Two Variables
Geometry 3.4 Big Idea: Find the Slope of a Line. Determine if lines are parallel or perpendicular.
1 What you will learn today 1. Review of slope 2. How to determine slope 3. How to graph a linear equation in y = mx + b form 4. Slopes of parallel and.
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.
Trigonometry/ Pre-Calculus Chapter P: Prerequisites Section P.3: Lines in the Plane.
Slopes of Equations and Lines Honors Geometry Chapter 2 Nancy Powell, 2007.
Section 1.1 Slopes and Equations of Lines
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.
Slope of a Line Chapter 7 Section 3. Learning Objective Find the slope of a line Recognize positive and negative slopes Examine the slopes of horizontal.
Linear Models & Rates of Change (Precalculus Review 2) September 9th, 2015.
3-7 Equations of Lines in the Coordinate Plane
Geometry: Parallel and Perpendicular Lines
C ollege A lgebra Linear and Quadratic Functions (Chapter2) 1.
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.
Section 6.6 What we are Learning:
Honors Geometry Section 3.8 Lines in the Coordinate Plane.
Lesson 5.5 OBJ: To write equations of parallel and perpendicular lines.
Linear Equations in Two Variables
What are the characteristics of Lines in the Plane? Section P4 (new text)
Honors Geometry Section 3.8 Lines in the Coordinate Plane.
2.2 SLOPE AND RATE OF CHANGE Algebra 2. Warm-up Learning Targets Students should be able to…  Find slopes of lines.  Classify parallel and perpendicular.
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.
TSW calculate slope given two points TSW calculate slope for parallel/perpendicular lines TSW write linear equations given slope and y-intercept TSW write.
Functions and Their Graphs 1.1 Lines in the Plane.
Copyright © 2011 Pearson Education, Inc. Linear Equations in Two Variables Section 1.4 Equations, Inequalities, and Modeling.
Copyright 2013, 2009, 2005, 2002 Pearson, Education, Inc.
Equations of Lines Standard Form: Slope Intercept Form: where m is the slope and b is the y-intercept.
2.2 Slope and Rate of Change, p. 75 x y (x1, y1)(x1, y1) (x2, y2)(x2, y2) run (x2 − x1)(x2 − x1) rise (y2 − y1)(y2 − y1) The Slope of a Line m = y 2 −
4.4 Slope of a Line. Slope – a measure of how steep a line is. Slope is the ratio of the vertical change to the horizontal change of a non- vertical line.
In your math notebook find the value of x so that the lines are parallel.
8.2 Lines and Their Slope Part 2: Slope. Slope The measure of the “steepness” of a line is called the slope of the line. – Slope is internationally referred.
Algebra 1 Notes Lesson 5-6: Parallel and Perpendicular 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.
2.6 Extension Writing Equations of Parallel and Perpendicular Lines.
Write Equations of Parallel and Perpendicular Lines
I can determine when lines are parallel and write equations of parallel lines.
Section 6.5: Parallel and Perpendicular Lines Objectives: Determine whether lines are parallel Determine whether lines are perpendicular Write equations.
4.5A Find and Use Slopes of Lines. Recall: The slope of a non-vertical line is the ratio of vertical change (rise) to horizontal change (run) between.
2 – 2: Slope and Rate of Change Objective: CA Standard 7.0: Students add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial.
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.
§ 7.3 Slope of a Line. Angel, Elementary Algebra, 7ed 2 Slope The slope of a line is the ratio of the vertical change between any two selected points.
Section 3-7 Equations of Lines in the Coordinate Plane Michael Schuetz.
3.6 and 3.7 slopes of ll and Lines. Standard/Objectives: Standard 3: Students will learn and apply geometric concepts. Objectives: Find slopes of lines.
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.
Slope of a Line. Slopes are commonly associated with mountains.
3.4 Find and use Slope of Lines. Slope Slope is: Rate of change A ratio of rise and run The change in Y over the change in X The m is Y = mX +b.
Everything You Will Ever Need To Know About Linear Equations* *Whether You Wanted To Know It Or Not!
The ratio of vertical change to horizontal change
Section 3.6 Find and Use Slopes of Lines
Presentation transcript:

Review of lines Section 2-A

Slope (m) of a line Let P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ) be points on a nonvertical line, L. The slope of L is

Slope measure steepness of a line The steeper the line the greater the absolute value of slope Lines that rise to the right have positive slopes Lines that fall to the right have negative slopes Horizontal lines have zero slopes Vertical lines have undefined slopes

Slope = Ratio If the x and y values have the same units, then the slope will have no units If the x and y values have different units, especially when x is in units of time, then slope will have units per time Slope = Rate of Change

Equations of lines Consider Multiply both sides by the denominator Point-slope form Suppose point one is The y-intercept (0,b) Slope-intercept form Standard/General form

Remember Vertical lines – the value of x does not change Horizontal lines – the value of y does not change and m = 0

Parallel (Tangent) and Perpendicular (Normal) Tangent lines – two lines with the same slope Normal lines – two lines that have slopes that are opposite reciprocals

1)Find the equation of the line through (6,8) that is parallel to 3x – 5y = 11 in slope-intercept form

2) Find the equation of the line through the point of intersection of the lines 3x + 4y = 8 and 6x – 10y = 7 that is normal to the first line in General form

3) Find an additional point through the line Choose an arbitrary value for x:

HOMEWORK Page 16 # 9,11,12,19,21,29-37, all May want to use graph paper

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2024 SlidePlayer.com Inc. All rights reserved.