1. From a graph and ordered pairs
The Slope of a Line
From a graph and ordered pairs

2. Focus 7 - Learning Goal #1: The student will understand the connections between proportional relationships, lines, and linear equations and use functions to model relationships between quantities. 4 3 2 1
In addition to level 3.0 and beyond what was taught in class, the student may:
Make connection with other concepts in math.
Make connection with other content areas.
The student will demonstrate and explain the connections between proportional relationships, lines, and linear equations and use functions to model relationships between quantities.
The student will demonstrate and identify proportional relationships, lines, and linear equations and use functions to model quantities.
With help from the
teacher, the student has
partial success with level 2 and 3 elements.
Even with help, students have no success with level 2 and 3 content.

3. Finding Slope of a Line
The method for finding the steepness of stairs suggests a way to find the steepness of a line.
A line drawn from the bottom step to the top set of a set of stairs touches each step in one point.
The rise and the run of a step are the
vertical and the horizontal changes, respectively, between two points on the line.

4. Finding the Slope of a Line
The steepness of the line is the ratio of rise to run, or vertical change to horizontal change, for this step.
We call the steepness of a line its slope.

5. Important things about slope…
Slope = rate of change = steepness of a line
Slope is a fraction of the change in y over change in x.
Slope is represented by the letter m
Vertical line has NO slope (it’s undefined)
Horizontal line has a slope zero (it’s 0)
change in y
change in x
rise
run or

6. 1. A line with a positive slope rises from left to right (m>0)
Classify lines by their slope: y x
1. A line with a positive slope rises from left to right (m>0)

7. 2. A line with a negative slope falls down from left to right (m<0)y x

8. 3. A line with a zero slope is horizontal (m=0) Equation y = 3x

9. 4. A line with an undefined slope is vertical (m is undefined) YOU CANT DIVIDE BY 0!x

10. To Find slope from a graph:
Find at least 2 clear points on the line
Starting on the furthest left point, count how many units up or down until you’re in line with the next point. That number will be numerator (top of fraction). If move up use positive (+), if move down use negative (–)
Then count how many units over to the right until you hit the next point. Than number will be denominator (bottom of fraction) -4
“Count it out”
A slope of -4/3 means down 4 over 3 from point to point 3

11. Find slope from a graph. down 3 -3 over 2 2 “Count it out”
Find at least 2 clear points on the line. Start on the left
Count how many units up or down
Count how many units over to the right
“Count it out”
down 3
over 2
down 3 -3
A slope of -3/2 means that for every time y goes down 3, x moves over 2 to the right
over 2 2

12. Find the slope by using the graph.
To find the slope, start with one point and count up how many rows it goes up and count how many rows it goes over. Make this a fraction and reduce if necessary.
This line goes up 2 and over 1.
The slope is 2/1 or 2.

13. Be Careful – What if each grid line isn’t just one unit??
Always check the intervals on the graph! Each line doesn’t have to be only one unit!
To find the slope, start with one point and count how many units it goes up and count how many units it goes over. Make this a fraction and reduce if necessary.
Over 2
Up 15
This line goes up 15 units and over 2 units.
The slope is 15/2 = 7.5

14. Formula for slope:

15. Find the slope of a line passing through points (-2,4) and (3,6)
To Find Slope from Points:
Find the slope of a line passing through points (-2,4) and (3,6)
(x1,y1)
(x2,y2)
1. Assign the first point as (x1,y1) and assign the second point as (x1,y1)
2. Use slope formula
6 - 4 2
3. Plug values in and simplify
m = =
3 - -2 5

16. Find the slope of a line passing through points (1,1) and (3,-2)
(x1,y1)
(x2,y2)
-2 - 1 3
m =
= -
3 - 1 2