1. SLOPE

2. 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

3. 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.

4. SLOPE
These 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).

5. 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. 4 5 3 1 2
vertically 5 3
horizontally 3 1 2
Slope =

6. SLOPE There are different names for the slope ratio. 5 Slope = 3 5 3 5
vertical change =
horizontal change 3 5
rise =
run 3
change in y 5 5 3 =
Slope =
change in x 3

7. Let’s look at the “sign” of the slope or the correlation.
“Going up the mountain.”
Slope = 5 3
positive slope
“Going down the mountain.”
Slope = 5 3 -
negative slope

8. - / - = + - / + = - Counting Slope + / + = + +/ - = - Positive Slope
Negative Slope
Counting up … rise and right … run
Counting up … rise and left … run
Counting down… rise and left … run
Counting down… rise and right … run
+ / + = +
- / - = +
+/ - = -
- / + = -

9. +5 +3 Finding slope on the coordinate plane. Slope = 3 5 +y
1) Plot points
(2, 4)
2) Draw line +3
3) Count vertically
(-3, 1) x
4) Count horizontally
Slope = 3 5 +
5) Write slope as a ratio

10. Finding slope on the coordinate plane.y
1) Plot points
2) Draw line -6
3) Count vertically
(-1, 2) +4 x
4) Count horizontally +4 -6 -2 3
Slope =
5) Write slope as a ratio =
(5, -2)

11. Find slope algebraically when given two points
Point 1: (x1, y1) Point 2: (x2, y2)
difference between the y coordinates
difference between the x coordinates
Slope =

12. Find slope algebraically when given two points
Point 1: (-1, 2) Point 2: (5, -2)
difference between the y coordinates
difference between the x coordinates
Slope =
-2 - 2
5 - -1
- 4 6
- 2 3
m = = =

13. Find the slope of the line containing the points (6, 7) and (8, 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 formula
Substitute into slope formula
Subtract the y coordinates
Subtract the x coordinates
m = -2

14. Example 2:
Find the slope of a line containing (-3, 6) and (-12, -9)

15. Example 3: Through the given point, (-4, -2), graph the line with a slope of 4.y
1) Plot point
2) Count slope +1
a) Count vertically
(-3, 2) +4
b) Count horizontally x 4 1
m = +
5) Plot new point
(-4, -2)
6) Draw line

16. The end