We think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Thank you!
Presentation is loading. Please wait.
Published byEdith Clifford
Modified over 2 years ago
Linear Equations in Two Variables Digital Lesson
Copyright © by Brooks/Cole, Cengage Learning. All rights reserved. 2 Equations of the form ax + by = c are called linear equations in two variables. The point (0,4) is the y-intercept. The point (6,0) is the x-intercept. x y 2 -2 This is the graph of the equation 2x + 3y = 12. (0,4) (6,0) Linear Equations
Copyright © by Brooks/Cole, Cengage Learning. All rights reserved. 3 y x 2 -2 The slope of a line is a number, m, which measures its steepness. m = 0 m = 2 m is undefined m = 1 2 m = - 1 4 Slope of a Line
Copyright © by Brooks/Cole, Cengage Learning. All rights reserved. 4 x y x2 – x1x2 – x1 y2 – y1y2 – y1 change in y change in x The slope of the line passing through the two points (x 1, y 1 ) and (x 2, y 2 ) is given by the formula The slope is the change in y divided by the change in x as we move along the line from (x 1, y 1 ) to (x 2, y 2 ). y 2 – y 1 x 2 – x 1 m =, (x 1 ≠ x 2 ). ( x 1, y 1 ) ( x 2, y 2 ) Slope Formula
Copyright © by Brooks/Cole, Cengage Learning. All rights reserved. 5 Example: Find the slope of the line passing through the points (2, 3) and (4, 5). Use the slope formula with x 1 = 2, y 1 = 3, x 2 = 4, and y 2 = 5. y 2 – y 1 x 2 – x 1 m = 5 – 3 4 – 2 = = 2 2 = 1 2 2 (2, 3) (4, 5) x y Example: Find Slope
Copyright © by Brooks/Cole, Cengage Learning. All rights reserved. 6 A linear equation written in the form y = mx + b is in slope-intercept form. To graph an equation in slope-intercept form: 1. Write the equation in the form y = mx + b. Identify m and b. The slope is m and the y-intercept is (0, b). 2. Plot the y-intercept (0, b). 3. Starting at the y-intercept, find another point on the line using the slope. 4. Draw the line through (0, b) and the point located using the slope. Slope-Intercept Form
Copyright © by Brooks/Cole, Cengage Learning. All rights reserved. 7 1 Example: Graph the line y = 2x – 4. 2. Plot the y-intercept, (0, - 4). 1.The equation y = 2x – 4 is in the slope-intercept form. So, m = 2 and b = - 4. 3. The slope is 2. The point (1, -2) is also on the line. 1 = change in y change in x m = 2 4. Start at the point (0, 4). Count 1 unit to the right and 2 units up to locate a second point on the line. 2 x y 5. Draw the line through (0, 4) and (1, -2). Example: y=mx+b (0, - 4) (1, -2)
Copyright © by Brooks/Cole, Cengage Learning. All rights reserved. 8 A linear equation written in the form y – y 1 = m(x – x 1 ) is in point-slope form. The graph of this equation is a line with slope m passing through the point (x 1, y 1 ). Example: The graph of the equation y – 3 = - (x – 4) is a line of slope m = - passing through the point (4, 3). 1 2 1 2 (4, 3) m = - 1 2 x y 4 4 8 8 Point-Slope Form
Copyright © by Brooks/Cole, Cengage Learning. All rights reserved. 9 Example: Write the slope-intercept form for the equation of the line through the point (-2, 5) with a slope of 3. Use the point-slope form, y – y 1 = m(x – x 1 ), with m = 3 and (x 1, y 1 ) = (-2, 5). y – y 1 = m(x – x 1 ) Point-slope form y – y 1 = 3(x – x 1 ) Let m = 3. y – 5 = 3(x – (-2)) Let (x 1, y 1 ) = (-2, 5). y – 5 = 3(x + 2) Simplify. y = 3x + 11 Slope-intercept form Example: Point-Slope Form
Copyright © by Brooks/Cole, Cengage Learning. All rights reserved. 10 Example: Write the slope-intercept form for the equation of the line through the points (4, 3) and (-2, 5). y – y 1 = m(x – x 1 ) Point-slope form Slope-intercept form y = - x + 13 3 1 3 2 1 5 – 3 -2 – 4 = - 6 3 Calculate the slope. m = Example: Slope-Intercept Form Use m = - and the point (4, 3). y – 3 = - (x – 4) 1 3
Copyright © by Brooks/Cole, Cengage Learning. All rights reserved. 11 Two lines are parallel if they have the same slope. If the lines have slopes m 1 and m 2, then the lines are parallel whenever m 1 = m 2. Example: The lines y = 2x – 3 and y = 2x + 4 have slopes m 1 = 2 and m 2 = 2. The lines are parallel. x y y = 2x + 4 (0, 4) y = 2x – 3 (0, -3) Example: Parallel Lines
Copyright © by Brooks/Cole, Cengage Learning. All rights reserved. 12 Two lines are perpendicular if their slopes are negative reciprocals of each other. If two lines have slopes m 1 and m 2, then the lines are perpendicular whenever The lines are perpendicular. 1 m1m1 m 2 = - or m 1 m 2 = -1. y = 3x – 1 x y (0, 4) (0, -1) y = - x + 4 1 3 Example: The lines y = 3x – 1 and y = - x + 4 have slopes m 1 = 3 and m 2 = -. 1 3 1 3 Example: Perpendicular Lines
Linear Equations in Two Variables Digital Lesson.
Pre-Algebra 11-2 Slope of a Line 11-2 Slope of a Line Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation.
Linear Functions. Review of Formulas Formula for Slope Standard Form Slope-intercept Form Point-Slope Form *where A>0 and A, B, C are integers.
1.4 Linear Equations in Two Variables. Definition of Slope The slope of the line through the distinct points (x 1, y 1 ) and (x 2, y 2 ) is where x 2.
Solving Linear Equations in One Variable Chapter 1 – Section 1.
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 ?
1 Equations of the form ax + by = c are called linear equations in two variables. The point (0,4) is the y-intercept. The point (6,0) is the x-intercept.
2.4 Writing the Equation of a Line. Review of Slope-Intercept Form The slope-intercept form of a linear equation is y = mx + b. m represents the slope.
Slope Problems. Slope Problem Examples Determine a value for x such that the line through the points has the given slope. Let's use the slope formula.
SLOPE AND RATE OF CHANGE EQUATIONS OF LINES Section 3.4 & 3.5.
WRITING AN EQUATION OF A LINE DETERMINE THE EQUATION OF A LINE AND/OR GRAPH A LINEAR EQUATION.
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.
Writing Equations of a Line. Various Forms of an Equation of a Line. Gradient-Intercept Form Standard Form Point-Gradient Form.
2.4 Write Equations of Lines Date: 9/4 Objective: Use point slope formula to write and equation of a line.
SLOPE Objectives: Find the slope of a line given the coordinates of two points on the line Graph equations using y=mx+b form.
Parallel & Perpendicular Slopes II Unit 6. Warm Up Which of these lines are parallel? Why? Which are perpendicular? Why? a) y = 2x + 3 b) y = 2x + 3 c)
Parallel and Perpendicular Lines. Slope-Intercept Form Useful for graphing since m is the slope and b is the y-intercept Point-Slope Form Use this form.
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.
Chapter 5 Review. Slope Slope = m = = y 2 – y 1 x 2 – x 1 Example: (4, 3) & (2, -1)
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.
Algebra II 2.2: Find slope and rate of change HW: p.86 (4-8 even, even) Quiz : Wednesday, 10/9.
Parallel and Perpendicular Lines Honors Math – Grade 8.
Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.
Point-Slope Formula Writing an Equation of a line Using the Point-Slope Formula.
WRITE EQUATIONS OF PARALLEL AND PERPENDICULAR LINES November 20, 2008 Pages
Linear Equations Objectives: -Find slope of a line - Write 3 different forms of linear equations Mr. Kohls.
Point-Slope Form Linear Equations in Two Variables.
Parallel and Perpendicular Lines. Warm – up!! * As you walk in, please pick up a calculator and begin working on your warm –up! 1.What is the formula.
MATHPOWER TM 10, WESTERN EDITION Equations of Linear Relations Lesson
Copyright © Cengage Learning. All rights reserved. 1.1 Lines in the Plane.
WARM UP 1. Explain how to graph a linear equation written in slope-intercept form. 2. Explain how to graph a linear equation written in point-slope form.
Graph a linear equation Graph: 2x – 3y = -12 Solve for y so the equation looks like y = mx + b - 3y = -2x – 12 Subtract 2x to both sides. y = x + 4 Divide.
Writing Equations Index Card Activity. I. How to Write an Equation of a Line Given m and b 1. Write down y = m x + b 2. Substitute slope for m and y-intercept.
Notes Over 2.1 Graphing a Linear Equation Graph the equation.
Graphing Using Slope - Intercept STEPS : 1. Equation must be in y = mx + b form 2. Plot your y – intercept ( 0, y ) 3. Using your y – intercept as a starting.
1.Use the given points to find the following: (8, 4) and ( 4, 5) a)Find the slope of the line that goes through the two points. 3 4 ( 4) ( 5) 8 4 – –
4.7 Graphing Lines Using Slope Intercept Form Goal: Graph lines in slope intercept form.
Straight Line Equation. x y x y y = -2x + 3. The Video Shop. You join a video shop for a membership fee of £3 and then charges £2 for each video you hire:
UNIT 1B LESSON 2 REVIEW OF LINEAR FUNCTIONS. Equations of Lines The horizontal line through the point (2, 3) has equation The vertical line through the.
Writing Linear Equations Using Slope Intercept Form.
Algebra 2 Lesson 2-4 Writing Linear Equations. Different Forms of Linear Equations Slope-intercept Form: y = mx + b Standard Form: Ax + By = C Point-Slope.
What is slope intercept form? What are parallel lines? What is point slope form? What is standard form? Warm up.
1.2 Linear Equations in Two Variables Writing linear equations.
Graphing Lines Objectives Find the slope of a line Given an equation of a line, graph the line Find the x-intercept and y-intercept of a line.
Holt McDougal Algebra Point-Slope Form Graph a line and write a linear equation using point-slope form. Write a linear equation given two points.
SLOPE LESSON 2-3 Algebra 2. Slope Slope basically describes the steepness of a line If a line goes up from left to right, then the slope has to be.
© 2017 SlidePlayer.com Inc. All rights reserved.