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The Slope Of A Line Objective: To find the slope of a line and to graph a line given its slope and a point.
What is slope? There are several definitions, but they are all related. Rate of change
Example y x Distance in miles Time In hours (x 1,y 1 ) (x 2,y 2 ) run = x 1 – x 2 rise = y 1 – y 2 m = rise/run = (y 1 – y 2 )/(x 1 – x 2 ) = miles/hour
Find the slope between the two points (2, 4) and (5, 1) (-3, 1) and (6, 4) (2, 3) and (-1, 3) (-2, 5) and (-2, 7) m = -1 m = 1/3 m = 0 No slope or undefined slope
Theorem The slope of a line in standard form Ax + By = C is -A/B
Point Slope Form y – y 1 = m(x – x 1 ) Variation: y = y 1 + (x – x 1 )m
Graph The Line Passing Through (1,2) with a slope m = ¼ Start by graphing the point (1,2) Since slope is rise over run move up 1 unit and right 4 units -4 -3 -2 -1 43214321 1 2 3 4 5 6 -2 -3 -4
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.
Example 2 Positive and Negative Slope Find the slope of the line. a. = run rise m = x1x1 x2x2 y1y1 y2y2 – – – – = 4 5 =
Warm-Up. Slope Slope Objectives: Define slope as the ratio of vertical rise to horizontal run. Determine the slope of a line given a graph. Determine.
WRITING LINEAR EQUATIONS FINDING THE SLOPE OF A LINE.
Objective- To find the slope of a line given two points. Graph y = 2x - 3 x y x y y = 2x - 3.
Less 5-1 Slope. Math Vocabulary Slope: The diagonal “slope” of a line on a graph that runs through given points.
Do Now Find the slope of the line passing through the given points. 1)( 3, – 2) and (4, 5) 2)(2, – 7) and (– 1, 4)
Objective - To find the slope of a line. Slope -The rate of change that determines the direction of a line and how steep it is. Slope = vertical change.
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.
5-2 Direct Variation A direct variation is a relationship that can be represented by a function in the form y = kx, where k ≠ 0. The constant of variation.
Notes Over 2.1 Graphing a Linear Equation Graph the equation.
Chapter 4 – Graphing Linear Equations 4.4 – The Slope of a Line.
Slope Formula. P1: ( -4, -5) P1: ( x 1, y 1 ) X 1 = -4, y 1 = -5 P2:( 4, 2) P2: (x 2, y 2 ) X 2 = 4, y 2 = 2 ( -4, -5) & ( 4,2)
Direct Variation Honors Math – Grade 8. Get Ready for the Lesson It costs $2.25 per ringtone that you download on your cell phone. If you graph the ordered.
3.3 Find Slope and Rate of Change Objective: Students will be able to find the slope of a line and interpret slope as a rate of change.
Warm UpOct. 15 For numbers 1-3, find the slope of the line that passes through each pair of points 1. (-4, -1) and (-3, -3) 2. (-2, 3) and (8, 3) 3.
Lesson 1-3: Formulas 1 Lesson 1-3 Formulas. Lesson 1-3: Formulas 2 The Coordinate Plane In the coordinate plane, the horizontal number line (called the.
These lines look pretty different, don't they? What is Slope?
Slope and Linear Equations Algebra I. Vocabulary Linear Equation – The equation of a line. Y intercept – where the line crosses the y axis. X intercept.
LEARNING TARGETS: 1. TO IDENTIFY SLOPE FROM A TABLE OF VALUES. 2. TO IDENTIFY SLOPE FROM A GRAPH. 3. TO IDENTIFY SLOPE FROM 2 POINTS. 4. TO IDENTIFY SLOPE.
Lesson 2: The Equation of a Line The Equation of a Line is: y = mx + b Where m is the slope And b is the y-intercept.
Warm Ups (Monday 4/13) Label the slopes of the lines as “Positive” or “Negative” or “Zero” or “Undefined”
Slope of a Line Chapter 7.3. Slope of a Line m = y 2 – y 1 x 2 – x 1 m = rise run m = change in y change in x Given two points (x 1, y 1 ) and (x 2, y.
The Slope of a Line. Important things about slope… Slope is the change in y over change in x. Slope is represented by the letter m Vertical line has NO.
5.1 Rate of Change and Slope Rate of Change: The relationship between two changing quantities Slope: the ratio of the vertical change (rise) to the horizontal.
Writing linear equations given two points /5/13.
SLOPE LESS 5-1. MATH VOCABULARY Slope: The diagonal “slope” of a line on a graph that runs through given points.
Writing Equations of Lines. Find the equation of a line that passes through (2, -1) and (-4, 5).
Sullivan Algebra and Trigonometry: Section 2.3 Lines Objectives Calculate and Interpret the Slope of a Line Graph Lines Given a Point and the Slope Use.
Slope (Finding it from a graph.). Key Idea : Slope of a line is a ratio of change in y (the rise) to the change in x (the run) between any two points.
5-1 Rate of Change and Slope Hubarth Algebra. Rate of change allows you to see the relationship between two quantities that are changing. If one quantity.
A proportional relationship between two quantities is one in which the two quantities vary directly with one another. Example: If one item is doubled,
Copyright © 2010 Pearson Education, Inc. All rights reserved Sec Slope of a Line.
Slopes of Equations and Lines Honors Geometry Chapter 2 Nancy Powell, 2007.
12/23/ : Slopes of Lines 1 Expectation: You will calculate slopes of lines parallel and perpendicular to given lines.
2.2 Linear Equations. SLOPE RISE RUN SLOPE Slope Formula Given points (X 1,Y 1 ) and (X 2,Y 2 ) Is the same as ?
The Slope of a Line 4.4 Objective 1 – Find the slope of a line using two of its points Objective 2 – Interpret slope as a rate of change in real-life situations.
Thinking Mathematically Algebra: Graphs, Functions and Linear Systems 7.2 Linear Functions and Their Graphs.
Introduction To Slope. Slope is a measure of Steepness.
Lesson 6-6 Example Example 2 Graph y = 3x + 2 and determine the slope of the line. 1.Complete a function table for the equation.
DEFINING SLOPE SECTION 5.2 Slope = = ________ is the ratio of vertical ______ to horizontal _____. Sloperise run rise SLOPEMAN My one weakness is that.
Lesson 4-4 Example Determine the slope of the function y = 5x – 2. Step 1Complete a function table for the equation.
Holt McDougal Algebra Graphing Linear Functions Toolbox 2.3 (a)
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 −
03.03 SKM & PP 1 Slope SKM & PP 2 Definition: Slope The slope of the line containing points P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ) is given by The.
Rate of Change and Slope Monday, November 1, 2010.
LEQ: What is the process used to graph direct variation equations?
M Linear equations also known as lines. m Each line is defined by: intercepts and slope m Slope is the change in y over the change in x m rise over run.
Slope and Direct Variation Lesson 5-2. ____________ ______________ is an equation in the form of ________, where k≠0. In the equation y = kx, ____ is.
EXAMPLE 2 Graph direct variation equations Graph the direct variation equation. a.a. y = x 2 3 y = –3x b.b. SOLUTION a.a. Plot a point at the origin. The.
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