Download Document

Section 1.4
Lines
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Find the slope of the line containing the points (-1, 4) and (2, -3).
3  4
7
m

2 1
3
43
7
m

1  2
3
7
The average rate of change of y with respect to x is 
3
Copyright © 2013 Pearson Education, Inc. All rights reserved
Compute the slopes of the lines L1, L2, L3, and L4 containing the
following pairs of points. Graph all four lines on the same set of
coordinate axes.
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Graph the equation: x = –2
y

(-2,4)

(-2,2)


(-2,0)


(-2,1)
x





Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Find the equation of a line with slope –3 and containing
the point (–1, 4).
y  4  3  x   1 
y

y  4  3x  3
Run = 1

Rise = -3

y  3 x  1

x







Copyright © 2013 Pearson Education, Inc. All rights reserved
Find the equation of a horizontal line containing the point
(2, – 4).
y   4  0   x  2
y

x
y40
y  4










Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Find an equation of the line L containing the points (–1, 4) and
(3, –1). Graph the line L.
5
y  4    x   1 
4
5
y  4    x  1
4
5
1  4

m
4
3   1

(-1, 4)




    







(3, -1)



Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Find the slope m and y-intercept b of the equation
3x – 2y = 6. Graph the equation.
3x – 2y = 6
– 2y = –3x+6



3
y  x 3
2


    

(2, 0)
2





3
3
y  x 3
2


(0, -3)

Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Graph the linear equation 3x + 2y = 6 by finding its
intercepts.
3x + 2(0) = 6
3(0) + 2y = 6

3x = 6
2y = 6
x=2
y=3

(0, 3)


    


The x-intercept is at the point (2, 0)
(2, 0)





The y-intercept is at the point (0, 3)



Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
L1 :  3x  2 y  12
L2 : 6 x  4 y  0
2 y  3 x  12
3
y  x6
2
3
Slope  ; y -intercept  6
2
4 y  6 x
3
y x
2
3
Slope  ; y -intercept  0
2
y






x











Copyright © 2013 Pearson Education, Inc. All rights reserved
Find an equation for the line that contains the point (1,3) and is
parallel to the line 3x  4 y  12.
4 y  3x  12.
y  y1  m  x  x1 
y


3
y  x 3
4


x








3
y  3   x  (1) 
4
3
15
y  x
4
4


3
So a line parallel to this one would have a slope of .
4
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Find the slope of a line perpendicular to a line with slope
4
m2  
3
mperpendicular
4

3

m1 


3
4
.
3
4


    










Copyright © 2013 Pearson Education, Inc. All rights reserved
Find an equation for the line that contains the point (1,3) and is
perpendicular to the line 3x  4 y  12.
y  y1  m  x  x1 
4 y  3x  12.
y

3
y  x 3
4



x








4
y  3    x  (1) 
3
4
5
y  x
3
3


4
So a line perpendicular to this one would have a slope of  .
3
Copyright © 2013 Pearson Education, Inc. All rights reserved