Download 13.2 Slope of a Line

Geometry
13.2 Slope of a Line
Review of Lines:
1. How many points determine a line?
2
2. How many points are on a line?
an infinite number of points
3. For every value of x, will there be a
value of y?
yes
Finding Slope
change in y
Slope =
change in x
vertical change
=
horizontal change
rise
=
run
Subtract
numerator and
denominator in
the same order
y2 – y1
=
x2 – x1
4-1
3
=
=
5-3
2
∆y
∆x
2
3
●
(5,4)
● (3,1)
Example 1a: Find the slope of the
line.
y
slope = y2 – y1
x2 – x1
=
=
=
4 – (-2)
5-1
6
4
3
2
.
(5 , 4)
x
.
(1 , -2)
3
__
The slope of the line is 2
Example 1b: Find the slope of the line.
slope
=
=
=
y
y2 – y1
x2 – x1
-5 – (-2)
3 – (- 1)
-3
4
(-1 , -2)
x
.
.
(3 , -5)
3
__
The slope of the line is - 4
POSITIVE slopes rise as you move from
left to right.
uphill
NEGATIVE slopes fall as you move from
left to right.
downhill
Do #1 and #4 from your notes and check
them below using the formula. You have
one minute…….
1. m = -5/4
4. m = 2/3
uphill or downhill?
uphill or downhill?
Example 2a. Find the slope of the
line.
y
slope = y2 – y1
x2 – x1
=
=
=
5– 5
3 – (-4)
0
3+4
.
(-4 , 5)
.
(3 , 5)
x
It’s like jogging on flat ground, your slope is zero.
0
7 The slope of the line is 0.
All horizontal lines have a zero slope.
Example 2b. How about this slope?
slope
=
=
=
y2 – y1
x2 – x1
It’s like going up in an elevator, your rise can be
anything, but your run is zero. y
4 – (-1)
2-2
5
0
.(2 , 4)
. (2 , -1)
x
The slope of the line is undefined.
All vertical lines have an undefined slope.
Every type of slope.
Positive Slope
Greater than 1
Positive Slope
Less than 1
Uphill
Uphill
Steep
Flatter
Negative Slope
Greater than 1
Negative Slope
Less than 1
Slope = 0
Undefined Slope
Running up the
hill is undefined!
Downhill
Downhill
Steep
Flatter
Exercise #12:
Find the slope and length of AB.
A (4, -2)
B (5, -3)
slope:
-3 – (-2)
-1
=
m=
5-4
1
length:
d = (5 - 4) +(-3 - (-2))
2
=
1 +(-1)
2
2
2
= √2
= -1
The slope of a line segment is constant. No matter which two
points you choose on the line, you will get the same value for m.
You can use this property to find other points on the same line.
Example 3a
a. Find 3 other points on the line that passes through
P(1, 2) and has slope 2/3.
•
•
•
•
Plot the point (1,2).
From there, rise 2 and run 3 to get
another point. (4, 4)
From there, rise 2 and run 3 to get
another point. (7, 6)
You can also go back to (1,2) and from there rise -2 and run -3
to get to the point (-2, 0)
Example 3b
y ).
A line with slope 4/3 passes through points (4, -5) and (-2, -13
__
4
=
3
y – (-5)
4
=
3
y+5
-6
-2 – 4
Use the slope formula
to find the missing y
coordinate.
Simplify and solve as a proportion
-24 = 3y + 15
-39 = 3y
y = -13
Do Exercises #18 and #21 from your
notes and check them with the answers
below.
18. (7, -1) (-1, -3) (-5, -4)
19. The missing y coordinate is 4.
Homework
pg.