10. 2x – 5 > x; x > 5
24. x = 6; y = 6
11. 9x – 3 > 6x + 5; x > 8/3
31. C
12. X = 45; y = 60
32. F
13. X = 6; y = 15
33. B
14. X = 25; y = 40
34. C
15. X = 60; y = 60
40. 152°
16. Yes
41. 25°
17. No
42. 155°
18. No
43. Conv. Alt Ext Angles
19. No
44. Conv. Alt Int Angles
20. Yes
45. Conv. Same-Side Int Angles
21. yes
Warm Up
Find the value of m.
1.
2.
3.
4.
undefined
0
The slope of a line in a coordinate plane is a
number that describes the steepness of the line.
Any two points on a line can be used to determine
the slope.
Remember!
A fraction with zero in the denominator is undefined
because it is impossible to divide by zero.
Example 1: Use the slope formula to determine
the slope of each line.
AB
AC
AD
The slope is undefined.
CD
One interpretation of slope is a rate of change. If
y represents miles traveled and x represents time
in hours, the slope gives the rate of change in
miles per hour.
Example 2:
Justin is driving from home to his college
dormitory. At 4:00 p.m., he is 260 miles from home.
At 7:00 p.m., he is 455 miles from home. Graph the
line that represents Justin’s distance from home at
a given time. Find and interpret the slope of the
line.
Use the points (4, 260) and
(7, 455) to graph the line and
find the slope.
The slope is 65, which means
Justin is traveling at an average
of 65 miles per hour.
Another way to look at perpendicular slopes is OPPOSITE
RECIPROCALS, meaning 2/3 and -3/2.
Example 3a
Graph each pair of lines. Use slopes to determine
whether the lines are parallel, perpendicular, or
neither.
WX and YZ for W(3, 1),
X(3, –2), Y(–2, 3), and
Z(4, 3)
Vertical and horizontal lines are perpendicular.
Example 3b
Graph each pair of lines. Use slopes to determine
whether the lines are parallel, perpendicular, or
neither.
KL and MN for K(–4, 4),
L(–2, –3), M(3, 1), and
N(–5, –1)
The slopes are not the same, so the lines are not
parallel. The product of the slopes is not –1, so the
lines are not perpendicular.
Example 3c
Graph each pair of lines. Use slopes to determine
whether the lines are parallel, perpendicular, or
neither.
BC and DE for B(1, 1),
C(3, 5), D(–2, –6), and
E(3, 4)
The lines have the same slope, so they are parallel.