Slope – Parallel and Perpendicular Lines

Slides:

Advertisements

Similar presentations

U1B L1 Review of Slope UNIT 1B LESSON 1 Review of Slope.

Advertisements

3-5 Slopes of Lines Warm Up Lesson Presentation Lesson Quiz

SLOPE AND PARALLEL AND PERPENDICULAR LINES.

Parallel and Perpendicular Lines

2.2 Slope and Rate of Change

Writing Parallel and Perpendicular Lines Part 1. Parallel Lines // (symbol) All parallel lines have the same slope. Parallel lines will NEVER CROSS. Since.

2-3 Slope Slope 4 indicates the steepness of a line. 4 is “the change in y over the change in x” (vertical over horizontal). 4 is the ‘m’ in y = mx + b.

Geometry Section 3.6 “Slope of Parallel and Perpendicular lines”

Section 7.3 Slope of a Line.

2.2 Slope and Rate of Change Algebra 2 Mrs. Spitz Fall 2009.

Warm Up for 9.6 Find the distance and midpointbetween the following sets of points. (5, 19) and (-3, -1) (7, -16) and (-2, -1) (1, -4) and (0, 0) (-6,

Parallel and Perpendicular Lines

Slopes of Lines Chapter 3-3.

3.7 Perpendicular Lines in the Coordinate Plane

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.

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.

Answers to warm-up A: (-10, 6) B: (-4, -2) C: (0, -5) D: (3, 0) E: (7, 3)

11.6 Slope. Rate of Change – identifies the relationship between two #’s that are changing Slope – a line’s rate of change Slope formula =

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

Slope – Parallel and Perpendicular Lines Mrs. King and Ms. Reed Geometry Unit 12, Day 9

TODAY IN GEOMETRY…  STATs for Ch Quiz  Learning Goal 2: 3.4 Calculate Parallel and Perpendicular Slopes with a graph and algebraically  Independent.

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.

Parallel and Perpendicular Lines

Lines: Slope The slope of a line is the ratio of the vertical change to the horizontal change between any two points on the line. As a formula, slope =

3-7 Equations of Lines in the Coordinate Plane

Honors Geometry Section 3.8 Lines in the Coordinate Plane.

5-5 Coordinate Geometry Warm Up Problem of the Day Lesson Presentation

Honors Geometry Section 3.8 Lines in the Coordinate Plane.

3.4 – FIND AND USE SLOPES. Slope: measures the steepness of a line or the rate of change. Slope = m = Rise Run Up or down Left or right =

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.

C 4 up Page | 1 Olympic College - Topic 6 Cartesian Coordinates and Slopes Topic 6 Cartesian Coordinates and Slopes 1. Cartesian Coordinate System Definition:

Linear Functions Slope and y = mx + b. Remember Slope… Slope is represented by m m = 0 Horizontal Line Vertical Line Slope up to the right Slope up to.

Advanced Algebra Notes Section 2.2: Find Slope & Rate of Change The steepness of a line is called the lines The slope of a non-vertical line is: The slope.

Equations of Lines Standard Form: Slope Intercept Form: where m is the slope and b is the y-intercept.

The Slope of a Line. Finding Slope of a Line The method for finding the steepness of stairs suggests a way to find the steepness of a line. A line drawn.

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.

Holt McDougal Geometry 3-5 Slopes of Lines 3-5 Slopes of Lines Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson.

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.

3-5 Slopes of Lines Warm Up Lesson Presentation Lesson Quiz

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.

Warm Up Find the value of m undefined.

Slope Lesson 4.6.

§ 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.

Lesson 5-1. The ___________ of a line is a number determined by any two points on the line. It is the ratio of the ___________ (vertical change) over.

Algebra 3 Lesson 1.1 Objectives: SSBAT define slope. SSBAT calculate slope given 2 points. SSBAT determine the slope of a line from the graph. SSBAT determine.

Unit 2-2 Slope. What is slope? The _________ of a line in a coordinate plane is a number that describes the steepness of the line. Any ____ points on.

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.

Parallel and Perpendicular Lines

Chapter 2 Section 2 Part II

Slopes of lines.

Coordinate Geometry & Algebra Review

Algebra 1 Review Linear Equations

3.4 Find and Use Slopes of Lines

Parallel & Perpendicular Lines in the Coordinate Plane

Graphing Linear Equations

3-5 Slopes of Lines Warm Up Lesson Presentation Lesson Quiz

2.2 Slope and Rate of Change

2-3 Slope Slope is “the change in y over the change in x” (vertical over horizontal). rise / run is the ‘m’ in y = mx + b.

SLOPE SECTION 3-3 Spi.2.1.D Jim Smith JCHS.

Parallel and Perpendicular Lines

Section 3.6 Find and Use Slopes of Lines

Monday, October 18 Slope of a Line

SLOPE SECTION 3-3 Spi.2.1.D Jim Smith JCHS.

3-3 Slopes of Lines Slope is the ratio of the rise (the vertical change) over the run (the horizontal change). Sometimes they will give you a graph, pick.

3.5 Slopes of Lines.

Presentation transcript:

Slope – Parallel and Perpendicular Lines Geometry D – Chapter 3.3

Slope - Defined Given two points (x1, y1) and (x2, y2), the slope m of a line is defined to be:

Slope – Example #1 Given two points A(-3, -4) and B(3, 5), find the slope of the line through the points. Algebraically: Reduce fractions whenever possible.

Slope – Example #1 Given two points A(-3, -4) and B(3, 5), find the slope of the line through the points. Graphically: Graph the line through the points. B Construct a right triangle. Going from A to B, count the change in x and y. 9 A 6

Slope – Example #2a Algebraically, find the slope of the line AB. The slope of the line through AB is 3/5.

Slope – Example #2b Graphically, find the slope of the line CD. Going from C to D, the line goes down 3 and left 2. -3 -2 The slope of the line is 3/2.

Slope – Example #2b The slope of line AB is 3/5. The slope of line CD is 3/2. Compare line AB and line CD. What can you say about them? The slope of line CD is greater than line AB. Line CD is steeper than line AB.

Slope – Example #2c On your own: Find the slope of EF. Compare it with AB and CD. The slope of EF is -2/3. Since the slope is negative, the line runs down as we look from left to right. Positive slope runs up from left to right. Using the absolute values of the slopes. Therefore AB is not as steep as EF which is not as steep as CD.

Slope – Example #2d On your own: Find the slope of CF. C(3,7) F(3, -6) Since division by zero is not defined, the slope of CF is undefined.

Slope – Vertical Lines The slope of any vertical line is undefined.

Slope – Example #3 On your own: Find the slope of MN. M(-1, 2) N(3, 2) The slope of MN is 0. MN is said to have zero slope.

Slope – Horizontal Lines The slope of any horizontal line is zero.

Slope – Other Lines Find the slope of PQ, RS, and TU. Allow time for student work! What can be said about lines PQ and RS? The lines are parallel and have the same slope.

Slope – Parallel Lines Parallel lines have equal slopes.

Slope – Other Lines What can be said about lines PQ and TU? Use pages 1-2 of GSP file 3_3_pptdemo here! The lines are perpendicular and have slopes which multiply to -1.

Slope – Perpendicular Lines Perpendicular lines have slopes which: multiply to -1 are negative reciprocals of each other. Horizontal and vertical lines are perpendicular to each other.

Slope – Example #4 Points R(3, -2) and S(-1, 3) form a line. a) find the slope of RS. b) find the slope of a line perpendicular to RS. Since perpendicular lines have slopes which are negative reciprocals, the slope of the perpendicular line is 4/5.

Slope – Example #4 Points R(3, -2) and S(-1, 3) form a line. c) knowing the slope of RS is -5/4, find another point on line RS. The slope of -5/4 indicates a change of -5 in the y direction and 4 in the x direction. X = 3 + 4 = 7 Y = -2 + (-5) = -7 Another point on the line is (7, --7)

Slope – Example #4 Points R(3, -2) and S(-1, 3) form a line. Can you find a similar point using S? Since we can also move 5 units in the y direction and -4 units in the x direction. From Point S, X = -1 + (-4) = -5 Y = 3 + 5 = 8 Another point on the line is (-5, 8)

Slope – Example #4 Points R(3, -2) and S(-1, 3) form a line. d) knowing the slope of RS is -5/4, find the slope of the line perpendicular to RS. Slopes of perpendicular lines are negative reciprocals of each other. The reciprocal of -5/4 is 4/5 or

Slope – Example #5 Points P(2, 5) and Q(4, y) form a line with a slope of 2/3. Find the value of y.