Slide 3.4- 1 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 1.
25
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 1
-
Upload
sharleen-reed -
Category
Documents
-
view
214 -
download
1
Transcript of Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 1.
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 1
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 2
Graphs of Linear Equations and Inequalities; Functions
Chapter 3
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 3
3.4
Equations of Lines
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 4
3.4 Equations of Lines
Objectives
1. Write an equation of a line given its slope and y-intercept.
2. Graph a line given its slope and a point on the line.
3. Write an equation of a line given its slope and any 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.
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 5
Write an equation of a line given slope and y-intercept.
3.4 Equations of Lines
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 6
3.4 Equations of Lines
Example 1 Write an equation of the line with slope 2/3 and y-intercept (0, 1).
Write an equation of a line given slope and y-intercept.
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 7
3.4 Equations of Lines
Graph a line given its slope and a point on the line.
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 8
3.4 Equations of Lines
Example 2 Graph 2x – 3y = 3 by using the slope and y-intercept.
(continued)
Graph a line given its slope and a point on the line.
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 9
3.4 Equations of Lines
Example 2 Graph 2x – 3y = 3 by using the slope and y-intercept.
(continued)
Graph a line given its slope and a point on the line.
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 10
3.4 Equations of Lines
Example 2 Graph 2x – 3y = 3 by using the slope and y-intercept.
Graph a line given its slope and a point on the line.
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 11
3.4 Equations of Lines
Example 4 Write an equation, in slope-intercept form, of the line having slope 4 passing through (2, 5).
Write an equation of a line given its slope and any point on the line.
Substitute x = 2, y = 5 and the given slope m = 4 into y = mx + b and solve for b.
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 12
3.4 Equations of LinesWrite an equation of a line given its slope and any point
on the line.
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 13
3.4 Equations of Lines
Example 5b Write an equation of the line through (4, 2), with slope 3/5. Give the final answer in slope-intercept form.
Write an equation of a line given its slope and any point on the line.
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 14
3.4 Equations of Lines
Example 6 Write an equation of the line through the points (2, 5) and (3, 4). Give the final answer in slope-intercept form.
Write an equation of a line given two points on the line.
Now use either point and the point-slope form. Using (3, 4) gives
(continued)
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 15
3.4 Equations of Lines
Example 6 Write an equation of the line through the points (2, 5) and (3, 4). Give the final answer in slope-intercept form.
Write an equation of a line given two points on the line.
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 16
3.4 Equations of Lines
Write an equation of a line given two points on the line.
Ax + By = C, called standard form, where A, B, and C are real numbers and A and B are not both 0. In most cases, A, B, and C are rational numbers.
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 17
3.4 Equations of Lines
Example 7a Find the equation in slope-intercept form passing through the point (4, 5) and (a) parallel to the line 2x + 3y = 6; (b) perpendicular to the line 2x + 3y = 6.
Write an equation of a line parallel or perpendicular to a given line.
Find the slope of the line 2x + 3y = 6.
(continued)
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 18
3.4 Equations of Lines
Example 7a Find the equation in slope-intercept form passing through the point (4, 5) and parallel to the line 2x + 3y = 6
Write an equation of a line parallel or perpendicular to a given line.
Parallel lines have the same slope. Use the point-slope form.
(continued)
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 19
3.4 Equations of Lines
Example 7a Find the equation in slope-intercept form passing through the point (4, 5) and parallel to the line 2x + 3y = 6
Write an equation of a line parallel or perpendicular to a given line.
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 20
3.4 Equations of Lines
Example 7b Find the equation in slope-intercept form passing through the point (4, 5) and perpendicular to the line 2x + 3y = 6.
Write an equation of a line parallel or perpendicular to a given line.
The slope of the line is –2/3. A line that is perpendicular must have a slope that is the negative reciprocal or 3/2.
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 21
3.4 Equations of Lines
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 22
3.4 Equations of Lines
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 23
3.4 Equations of Lines
Example 8a It is time to fill your car with gasoline. Gas is selling for $4.50 per gallon. Write an equation that describes the cost y to buy x gallons of gas.
Write an equation of a line that models real data.
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 24
3.4 Equations of Lines
Example 8b You can also get a car wash at the gas station if you pay an additional $3.00. Write an equation that defines the price for gas and a car wash.
Write an equation of a line that models real data.
Since an additional $3.00 will be charged, you pay $4.50x + 3.00 dollars for x gallons of gas and a car wash.
Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 25
3.4 Equations of Lines
Example 8c Interpret the ordered pairs (5, 25.5) and (10, 48) in relation to the equation from part b.
Write an equation of a line that models real data.
The ordered pair (5, 25.5) indicates that the price of 5 gal of gas and a car wash is $25.50. Similarly, (10, 48) indicates that the price of 10 gal of gas and a car wash is $48.00.
