Section 1.8 Homework questions?

Section

Concepts

1.8 Linear Equations in Two Variables

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1. Definition of a Linear Equation in Two Variables2. Graphing Linear Equations in Two Variables by

Plotting Points3. x- and y-Intercepts4. Horizontal and Vertical Lines

DEFINITION Linear Equation in Two Variables

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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.

Example 1 Determining Solutions to a Linear Equation

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For the linear equation 4x – 5y = 8, determine whether the given ordered pair is a solution.

Example 2 You Try

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For the linear equation 3x – 2y = -12, determine whether the given ordered pair is a solution.

a. (4, 0) b. (1, )15

2

Example 3 You Try

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1. Is (2, 2) a solution of 3x + 2y = 10?

2. Is (-3, 4) a solution of 3x + 2y = 10?

DEFINITION The Graph of an Equation in Two Variables

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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.

Section 1.8 Linear Equations in Two Variables

2. Graphing Linear Equations in Two Variables by Plotting Points

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The word linear means “relating to or resembling a line.”Because two points determine a line, to graph a linearequation it is sufficient to find two solution points and draw the line between them; finding a third point can be used to check accuracy.

PROCEDURE Graphing 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.

Example 4 Graphing a Linear Equation

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Graph the equation . 2 1y x

Example 5 Graphing a Linear Equation

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Graph the equation . 1

13

y x

Example 6 Graphing a Linear Equation

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Graph the equation 4

5.3

y x

DEFINITION x- and y-Intercepts

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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.

PROCEDURE Graphing 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.

PROCEDURE Finding x- and y-Intercepts

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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.

Example 7 Graphing a Linear Equation

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a. Find the x-intercept.b. Find the y-intercept.c. Graph the equation.

Example 8 Finding the x- and y-Intercepts of a Line

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Example 9 Finding the x- and y-Intercepts of a Line

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Given the equation 6x – 12y = 24

a.Find the x-intercept.b.Find the y-intercept.c.Graph the equation.

DEFINITION Equations of Vertical and Horizontal Lines

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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?

Example 10 Graphing a Horizontal Line

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Graph the equation y = 3.

Example 11 Graphing a Vertical Line

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Graph the equation 4x = –8.

Example 12 You Try

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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

11

2x

Example 12 You Try

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1. Graph y = 2x – 3

Example 12 You Try

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2. Graph y =1

12x

Example 12 You Try

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3. Find the x-intercept, y-intercept of x – 3y = -4

Example 12 You Try

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4. Graph 5y = -10

Example 12 You Try

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5. Graph x = 4

Section

Concepts

1.8 Linear Equations in Two Variables

Slide 28Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

1. Definition of a Linear Equation in Two Variables2. Graphing Linear Equations in Two Variables by

Plotting Points3. x- and y-Intercepts4. Horizontal and Vertical Lines

PROCEDURE Graphing 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.

PROCEDURE Graphing 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.

PROCEDURE Finding x- and y-Intercepts

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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.

PROCEDURE Equations of Vertical and Horizontal Lines

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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.