slope
DESCRIPTION
SLOPE. SLOPE. Slope is the “tilt” of the line. Slope is the “slant” of the line. zero slope. Positive slope Positive correlation. Negative slope Negative correlation. undefined slope. SLOPE. Slope is the steepness of the “slant” of the line. Slope is the steepness of a mountain side. - PowerPoint PPT PresentationTRANSCRIPT
SLOPE
SLOPESlope is the “tilt” of the line.Slope is the “slant” of the line.
Positive slope
Positive correlationNegative slope
Negative correlation
zero slope
undefined slope
SLOPE Slope is the steepness of the “slant” of the line. Slope is the steepness of a mountain side. Slope is the steepness of a wheelchair ramp. Slope is the steepness of a flight of stairs. Slope is the steepness of a plane’s decent. Slope is the steepness of a ski run. Slope is steepness of a skate board ramp.
SLOPEThese different slopes can be measured and
represented mathematically with a ratio. This ratio can be found by going from one
point on the line to another point by counting the vertical change and the horizontal change.
This ratio or slope is sometimes called the rise (vertical change) over the run (horizontal change).
Let’s investigate the steepness of this mountain slope.
#1) Pick two points on the side of the mountain.#2) Draw an imaginary grid.
#3) Count vertically and then horizontally from one point to the other.
vertically 12345horizontally
123 Slope =53
SLOPEThere are different names for the slope ratio.
vertical change 5horizontal change
3
Slope =53
rise run
5
3change in y
change in x
5
3
=
=
=
Let’s look at the “sign” of the slope or the correlation.
Slope =53
positive slope
Slope =53
-
“Going up the mountain.”
“Going down the mountain.”
negative slope
Counting Slope Positive Slope
Counting up … rise and right … run
Counting down… rise and left … run
+ / + = +- / - = +
Negative SlopeCounting up … rise and left … run
Counting down… rise and right … run
+/ - = -- / + = -
(2, 4)
(-3, 1)x
y
Finding slope on the coordinate plane.
1) Plot points
2) Draw line
3) Count - - vertically4) Count - - horizontally5) Write slope - as a ratio
+3
+5
Slope =35
+
(5, -2)
(-1, 2)
x
y
Finding slope on the coordinate plane.
1) Plot points
2) Draw line
3) Count - - vertically4) Count - - horizontally5) Write slope - as a ratio
+4
-6
Slope =+4-6
=-2 3
Find slope algebraically when given two points
my y
x x
( )
( )2 1
2 1
Point 1: (x1, y1) Point 2: (x2, y2)
Slope =difference between the y coordinatesdifference between the x coordinates
Find slope algebraically when given two points
Point 1: (-1, 2) Point 2: (5, -2)
Slope =difference between the y coordinatesdifference between the x coordinates
m =-2 - 2 5 - -1
- 4 6
- 2 3
= =
Example 1:
Find the slope of the line containing the points (6, 7) and (8, 3)
Remember each ordered pair is (x, y)Write slope formulaSubstitute into slope formula
Subtract the y coordinatesSubtract the x coordinates
m
( )
( )
7 3
6 8
m ( )
( )
4
2
m = -2
Example 2: Find the slope of a line containing (-
3, 6) and (-12, -9)
m
( )
( )
6 9
3 12
m ( )
( )
15
9
m 5
3
my y
x x
( )
( )2 1
2 1
(-3, 2)
(-4, -2)
x
y
Example 3: Through the given point, (-4, -2), graph the line with a slope of 4.
1) Plot point
2) Count slope
a) Count - - vertically
b) Count - - horizontally
5) Plot new . point
+4
+1
m =41
+
6) Draw line
The end