Ch 3

1
Ch 3

• Section 5 - Slope

2
(No Transcript)
3
Rate 10 per hour
1 hr
10
4
Rate 12.50 per hour
1 hr
12.50
5
Rate 12.50 per hour
Rate 10 per hour
6
Slope

• Slope a ratio that describes the steepness of a
  line and the direction that it slants.

y
2 units
?
3 units
?
x
7
Slope
Slope is relatively large positive.

• Slope a ratio that describes the steepness of a
  line and the direction that it slants.

y
Slope is relatively large negative.
Slope is relatively small positive.
Slope is relatively small negative.
x
8
Compute Slope when two points are known.

• Slope formula

?
?
9
Compute Slope

• Compute the slope of this line.

y
4 (-1)
-2 1
x
-1 4
1 (-2)
10
Compute Slope

• Compute the slope of this line.

y
4 0
4 3
x
0 4
3 4
11
Compute Slope

• Compute the slope of a line that passes through
  these two points.
• (-2,3) and (-6,5)

5
3
-6
-2
-
-
12
Horizontal Lines

• Compute the slope of this line.

y
y 2
2 2
0
5 (- 3)
x
13
Vertical Lines

• Compute the slope of this line.

y
x 4
5 (- 3)
Undefined
4 - 4
x
14
Summary

• Horizontal lines
• Slope 0
• Vertical lines
• Slope Undefined

?
0
?
0
15
Practice

• MathXL Ch 3 Section 5 Homework

16
Ch 3

• Section 6 Slope-Intercept Form

17
Introduction 1 of 2
4 ?

• Graph the line that passes through the point
  (0,2) and has a slope of m

?
3 ?
(0,2)
?
y-intercept
18
Introduction 2 of 2

• Graph the line that passes through the point
  (0,-1) and has a slope of m

(0,-1)
?
y-intercept
-2 ?
?
3 ?
19
Slope-Intercept Form

• Equations like these
• are in slope-intercept format.

20
Slope-Intercept Form
4
?
1
slope
?
y-intercept
y-intercept (0,2)
21
Slope-Intercept Form
slope 3
1
?
y-intercept (0,-5)
3
?
y-intercept
22
Slope-Intercept Form
slope
y-intercept
?
-2
y-intercept (0,-6)
?
3
23
Rearranging Equations to Slope-Intercept Form

• 2x y 1
• 2x 3y 9
• x 4y 12

• 2x y 1

-2x
-2x
y -2x 1

• 2x 3y 9

-2x
-2x
3y -2x 9
3 3 3
24
Rearranging Equations to Slope-Intercept Form

• 2x y 1
• 2x 3y 9
• x 4y 12

y -2x 1
-x
-x
x 4y 12
-4y -x 12
-4 -4 -4
25
Parallel Lines

• The two lines shown are parallel.
• What is the slope of each line?

8
3
8
3
26
Determine Parallel Lines 1 of 2

• Does this pair of equation represent parallel
  lines?
• y 3x 8
• y 3x -11

Yes, since the slopes are the same.
27
Determine Parallel Lines 2 of 2

• Does this pair of equation represent parallel
  lines?
• y 2x - 5
• 4x 2y 9

4x 2y 9
-4x -4x
No, since the slopes are different.
2y -4x 9
2 2 2
y -2x 9/2
28
Practice

• MathXL Ch 3 Section 6 Homework