This document discusses linear equations in two variables. It covers writing equations of lines given the slope and y-intercept, or given a point and the slope. It also discusses finding equations of lines parallel or perpendicular to a given line, or lines that model real data. The objectives are to write equations of lines in various scenarios and graph lines using different properties.

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Sec 4.3 - 1

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Sec 4.3 - 2
Graphs, Linear Equations,
and Functions
Chapter 4

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Sec 4.3 - 3
4.3
Linear Equations in Two Variables

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4.3 Linear Equations in Two Variables
Objectives
1. Write an equation of a line, given its slope and y-
intercept.
2. Graph a line, using its slope and y-intercept.
3. Write an equation of a line, given its slope and a
point on the line.
4. Write an equation of a line, given two points on
the line.
5. Write an equation of a line parallel or
perpendicular to a given line.
6. Write an equation of a line that models real data.

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4.3 Linear Equations in Two Variables
Write an equation of a line given its slope and y-intercept.
Given the slope m of a line and the y-intercept b of the
line, we can determine its equation.

6. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 4.3 - 6
4.3 Linear Equations in Two Variables
Write an equation of a line given its slope and y-intercept.
If we know the slope of a line and its y-intercept, we can
write its equation by substituting these values into the
above equation.

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4.3 Linear Equations in Two Variables
Writing an Equation of a Line

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4.3 Linear Equations in Two Variables
Graph Lines Using Slope and y-Intercept

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4.3 Linear Equations in Two Variables
Write an equation of a line, given its slope and a point on the line.
If we know the slope m of a line and the coordinates of a
point on the line, we can determine its equation.

10. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 4.3 - 10
4.3 Linear Equations in Two Variables
Write an equation of a line, given its slope and a point on the line.
If we know the slope of a line and the coordinates of a
single point on the line, we can write the equation of the
line by substituting these values into the equation above.

11. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 4.3 - 11
4.3 Linear Equations in Two Variables
Finding the Equation of a Line, Given the Slope and a Point

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4.3 Linear Equations in Two Variables
Finding an Equation of a Line, Given Two Points

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4.3 Linear Equations in Two Variables
Finding an Equation of a Line, Given Two Points

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4.3 Linear Equations in Two Variables
Equations of Horizontal and Vertical Lines

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4.3 Linear Equations in Two Variables
Finding Equations of Parallel or Perpendicular Lines
Recall that parallel lines have the same slope and
perpendicular lines have slopes with product –1.

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4.3 Linear Equations in Two Variables
Finding Equations of Parallel or Perpendicular Lines

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4.3 Linear Equations in Two Variables
Finding Equations of Parallel or Perpendicular Lines

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4.3 Linear Equations in Two Variables
Finding Equations of Parallel or Perpendicular Lines
6
–6
6
–6

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4.3 Linear Equations in Two Variables
Finding Equations of Parallel or Perpendicular Lines
Recall that parallel lines have the same slope and
perpendicular lines have slopes with product –1.

20. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 4.3 - 20
4.3 Linear Equations in Two Variables
Finding Equations of Parallel or Perpendicular Lines

21. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 4.3 - 21
4.3 Linear Equations in Two Variables
Finding Equations of Parallel or Perpendicular Lines

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4.3 Linear Equations in Two Variables
Finding Equations of Parallel or Perpendicular Lines
6
–6
6
–6

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4.3 Linear Equations in Two Variables
Forms of Linear Equations

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4.3 Linear Equations in Two Variables
Determining a Linear Equation to Describe Real Data
A veterinarian charges $45 to visit a farm where cattle are
raised. The price to vaccinate each animal is $18. Write
an equation that defines the total bill that the veterinarian
will submit to vaccinate all the cattle at the farm.