Download presentation

Presentation is loading. Please wait.

Published byIsabella Crowley Modified over 4 years ago

1
Section 1.8 Homework questions?

2
Section Concepts 1.8 Linear Equations in Two Variables Slide 2 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1.Definition of a Linear Equation in Two Variables 2.Graphing Linear Equations in Two Variables by Plotting Points 3.x- and y-Intercepts 4.Horizontal and Vertical Lines

3
DEFINITIONLinear Equation in Two Variables Slide 3 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Let A, B, and C be real numbers such that A and B are not both zero. Then, an equation that can be written in the form: Ax + By = C is called a linear equation in two variables. A solution of a linear equation in two variables is an ordered pair that makes the equation a true statement.

4
Example 1Determining Solutions to a Linear Equation Slide 4 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. For the linear equation 4x – 5y = 8, determine whether the given ordered pair is a solution.

5
Example 2You Try Slide 5 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. For the linear equation 3x – 2y = -12, determine whether the given ordered pair is a solution. a. (4, 0)b. (1, )

6
Example 3You Try Slide 6 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1.Is (2, 2) a solution of 3x + 2y = 10? 2.Is (-3, 4) a solution of 3x + 2y = 10?

7
DEFINITIONThe Graph of an Equation in Two Variables Slide 7 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The graph of an equation in two variables is a drawing of all ordered pair solutions to the equation. For a linear equation in two variables, the graph is a straight line.

8
Section 1.8 Linear Equations in Two Variables 2.Graphing Linear Equations in Two Variables by Plotting Points Slide 8 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The word linear means relating to or resembling a line. Because two points determine a line, to graph a linear equation it is sufficient to find two solution points and draw the line between them; finding a third point can be used to check accuracy.

9
PROCEDUREGraphing Linear Equations in the Form y = mx + b 1.Choose any value for x. 2.Plug it in and solve for y. 3.(x, y) is a solution to the equation. 4.Find two more solutions (ordered pairs). 5.Plot the points and draw the line connecting them.

10
Example 4Graphing a Linear Equation Slide 10 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Graph the equation.

11
Example 5Graphing a Linear Equation Slide 11 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Graph the equation.

12
Example 6Graphing a Linear Equation Slide 12 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Graph the equation

13
DEFINITIONx- and y-Intercepts Slide 13 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. An x-intercept of a graph is a point (a, 0) where the graph intersects the x-axis. A y-intercept of a graph is a point (0, b) where the graph intersects the y-axis.

14
PROCEDUREGraphing Ax + By = C We can use the x and y intercepts to graph equations where x and y are on the same side of the equation.

15
PROCEDUREFinding x- and y-Intercepts Slide 15 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Step 1 Find the x-intercept(s) by substituting y = 0 into the equation and solving for x. Step 2 Find the y-intercept(s) by substituting x = 0 into the equation and solving for y.

16
Example 7Graphing a Linear Equation Slide 16 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. a.Find the x-intercept. b.Find the y-intercept. c.Graph the equation.

17
Example 8Finding the x- and y-Intercepts of a Line Slide 17 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

18
Example 9Finding the x- and y-Intercepts of a Line Slide 18 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Given the equation 6x – 12y = 24 a.Find the x-intercept. b.Find the y-intercept. c.Graph the equation.

19
DEFINITIONEquations of Vertical and Horizontal Lines Slide 19 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1. A vertical line can be represented by an equation of the form, x = k, where k is a constant. 2. A horizontal line can be represented by an equation of the form, y = k, where k is a constant. Thinking ahead…. What does the line x = 4 look like? What does the line y = 4 look like? What does the line x = 0 look like? What does the line y = 0 look like?

20
Example 10Graphing a Horizontal Line Slide 20 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Graph the equation y = 3.

21
Example 11Graphing a Vertical Line Slide 21 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Graph the equation 4x = –8.

22
Example 12You Try Slide 22 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1.Graph y = 2x – 3 2.Graph y = 3.Find the x-intercept, y-intercept of x – 3y = -4 4.Graph 5y = -10 5.Graph x = 4

23
Example 12You Try Slide 23 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1. Graph y = 2x – 3

24
Example 12You Try Slide 24 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 2. Graph y =

25
Example 12You Try Slide 25 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 3. Find the x-intercept, y-intercept of x – 3y = -4

26
Example 12You Try Slide 26 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 4. Graph 5y = -10

27
Example 12You Try Slide 27 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 5. Graph x = 4

28
Section Concepts 1.8 Linear Equations in Two Variables Slide 28 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1.Definition of a Linear Equation in Two Variables 2.Graphing Linear Equations in Two Variables by Plotting Points 3.x- and y-Intercepts 4.Horizontal and Vertical Lines

29
PROCEDUREGraphing Linear Equations in the Form y = mx + b 1.Choose any value for x. 2.Plug it in and solve for y. 3.(x, y) is a solution to the equation. 4.Find two more solutions (ordered pairs). 5.Plot the points and draw the line connecting them.

30
PROCEDUREGraphing Ax + By = C We can use the x and y intercepts to graph equations where x and y are on the same side of the equation.

31
PROCEDUREFinding x- and y-Intercepts Slide 31 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Step 1 Find the x-intercept(s) by substituting y = 0 into the equation and solving for x. Step 2 Find the y-intercept(s) by substituting x = 0 into the equation and solving for y.

32
PROCEDUREEquations of Vertical and Horizontal Lines Slide 32 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1. A vertical line can be represented by an equation of the form, x = k, where k is a constant. 2. A horizontal line can be represented by an equation of the form, y = k, where k is a constant.

Similar presentations

OK

Squares and Square Root WALK. Solve each problem. 1. 2. REVIEW:

Squares and Square Root WALK. Solve each problem. 1. 2. REVIEW:

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google

Ppt on changes around us Ppt on search engine optimisation Ppt on rbi reforms in education Ppt on hindi grammar in hindi language View ppt on ipad mini Ppt online open enrollment Ppt on servant leadership Download ppt on teamviewer free Download ppt on social media marketing Ppt on culture heritage of india