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

Slides:

Advertisements

Similar presentations

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

Advertisements

Graphing Parallel and Perpendicular Lines

Parallel & Perpendicular Lines

7.8 Parallel and Perpendicular Lines Standard 8.0: Understand the concepts of parallel and perpendicular lines and how their slopes are related.

4.4 Parallel and Perpendicular Lines

Warm-Up On the same coordinate plane… ▫Graph the equation y=2x +3 ▫Graph the equation y=2x ▫Graph the equation y= - ½x + 1 What do you notice about the.

7.8 Parallel and Perpendicular Goals: To identify parallel, perpendicular lines and write an equation of a line containing a point and parallel or perpendicular.

2.4.2 – Parallel, Perpendicular Lines

Bellwork Partner Activity for graphing.

Bellwork 1. Given the two lines: y = 4x -2 and y =-1/4x +3. Are the two lines parallel, perpendicular or neither? 2. Write the equation of the line who.

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)

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)

The slope-intercept form of a linear equation of a non-vertical line is given by: Slope-Intercept Form of a Linear Equation.

Equations of lines.

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

2.3 Linear Functions.

Chapter 8 Graphing Linear Equations. §8.1 – Linear Equations in 2 Variables What is an linear equation? What is a solution? 3x = 9 What is an linear equation.

Writing Linear Equation using slope-intercept form.

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.

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.

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

3.6 Finding the Equation of a Line

3-7 Equations of Lines in the Coordinate Plane

Geometry: Parallel and Perpendicular Lines

Notes Over 5.3 Write an equation in slope-intercept form of the line that passes through the points.

OBJECTIVES: STUDENTS WILL BE ABLE TO… IDENTIFY IF 2 LINES ARE PARALLEL, PERPENDICULAR OR NEITHER GRAPH A LINE PARALLEL OR PERPENDICULAR TO ANOTHER WRITE.

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

WRITE EQUATIONS OF PARALLEL AND PERPENDICULAR LINES November 20, 2008 Pages

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

{ 2.4 Writing Equations of Lines.  Slope-Intercept Form:  Standard Form: Forms of Lines.

 When given the equation of a line that is perpendicular to the one you are interested in and a point on the line of interest, finding an equation for.

Lesson 5.5 OBJ: To write equations of parallel and perpendicular lines.

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

PARALLEL LINES Linear Equations. I can find the equation of a line parallel to a given line passing through a given point. Essential Question: Do you.

Find the slope through the points (5, 0) and (-10, 0)

Answers. Write the Formulas Slope Formula y₂-y₁ x₂-x₁ Point Slope Form y-y₁=m(x-x₁) Slope-intercept Form y=mx+b.

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.

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

Graphing Test Review Algebra.

5.6 Parallel and Perpendicular Lines

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

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 −

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.

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.

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

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.

Section 6.6 Parallel and Perpendicular Lines. Definitions Lines that lie in the same plane and never intersect are called parallel lines. All vertical.

Lesson 1-2 Slopes of Lines Object

Drill #23 Determine the value of r so that a line through the points has the given slope: 1. ( r , -1 ) , ( 2 , r ) m = 2 Identify the three forms (Point.

Parallel and Perpendicular Lines. 1. Fill in the chart with the missing slopes. (similar to p.234 #22) Slope of the Given Line Slope of a Line Parallel.

-last section we wrote an equation of a line using its slope and y-intercept -now, you will write an equation of a line.

Chapter 5 Review. Slope Slope = m = = y 2 – y 1 x 2 – x 1 Example: (4, 3) & (2, -1)

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.

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.

Write Equations of Parallel and Perpendicular Lines

POINTS AND LINES ON THE COORDINATE PLANE

Warm Up Find each y-intercept. 1. y = 3x x – 3y = 12

Math The Slope of a Line.

3.4 Notes: Equations of Lines

Writing Equations of Lines

Parallel and Perpendicular Lines

2.5 Linear Equations.

The Point-Slope Form of the Equation of a Line

3.4 Find and Use Slopes of Lines

3-6 Slopes of Parallel & Perpendicular Lines M11.B A

Presentation transcript:

Slope and Equations of Lines

Reviewing types of slope Remember, there are four types of slope: PositiveNegative No slope Undefined slope

The slope of a line  The slope of a nonvertical line passing thru the points (x 1,y 1 ) (x 2,y 2 ) :

Find the slope of a line passing thru (-3,5) & (2,1)

W/out graphing, tell whether the line thru the points is positive, negative, horizontal, or vertical.  1) (3,-4), (1,-6)  2) (2,-1), (2,5) Undefined: The line is vertical m>0, positive slope

What is the slope of the line? The constant, b = 3 is the y-intercept. The coefficient, m = -2 is the slope.

Fill in the Blank  Parallel Lines have the _______ slope.  Perpendicular Lines have slopes that are _________ __________.

Ex: y = 3x - 6 A. y = 2x + 1 B. y = 3x + 4 C. y = -3x + 6 D. y = Which equation is parallel? Which equation is perpendicular?

Ex: 4x – 8y = -16 A. y = 2x + 4 B. y = -2x - 1 C. y = -½x - 3 D. y = Which equation is parallel? Which equation is perpendicular?

Ex : Tell whether the lines are װ, ┴, or neither  L 1 : thru (-3,3) & (3,-1)  L 2 : thru (-2,-3) & (2,3) Negative reciprocals Of each other : They are ┴.

Equation of a Line  What is slope-intercept form?

Find the slope of the line y = 2x - 4. Slope-Intercept Form y = 2x The y-intercept is -4.

up 2 right 1 up 2 right 1

Example: Graph 3x + 4y = –12 Step 1: Put equation in slope – intercept form

Example  Write the equation of the line with slope = -2 and passing through the point (3, -5).  Substitute m and substitute into the Slope Intercept Form.  Y=-2x+b  -5=-2(3)+b  1=b  Y=-2x+1

Ex : Write the equation of the line with m=3 and through the point (2,-3)  Y=mx+b  Y=3x+b  -3=3(2)+b  -9=b

Write the Equation for the line:  Through (-2,1) and parallel to y=-3x+1  Plug the point (-2,1) into the equation y=mx+b 1=m(-2)+b  If it is parallel, then they have the same slope! So m=-3, therefore, 1 = (-3)(-2)+b 1 = 6+b =b  Write the equation of the new line: Y=-3x-5

Write the equation of the line:  Perpendicular to y=3x-4 that passes through the point (3,2).  2=m(3)+b  Slope is the neg. reciprocal so m=-1/3.  2=-(1/3)(3)+b  2=-1+b  3=bEquation: y=-1/3x+3

Parallel to the line 2x+y=6 thru (3,4).

Perpendicular to the line -3x+ y=4 thru (6,4)