1. Rate of Change
AKA
SLOPE

2. Types of Slopes

3. Negative Slope Lines that have negative slopes “slant downhill” as viewed from left to right.

4. Zero Slope Horizontal lines have Zero “slant” or SLOPE.

5. Positive Slope Lines that have positive slopes “slant uphill” as viewed from left to right.

6. No Slope Vertical lines have NO SLOPE or an Undefined Slope

7. Let’s Explore! We find Slope/Rate of change in various ways.
Method 1: By finding the Rise over the Run, typically used when finding the slope/rate of change of a graph.
Method 2: By finding the change in y values divided by the change in x values , typically used when finding the slope or rate of change in a table of data.
Method 3: By using the slope formula , typically used when given two points from a line.
Let’s Explore!

8. Slope AKA Rate of Change
is the measurement of steepness of a straight line.

9. Finding Slope /Rate of Change on a GRAPH
Rate of change or slope is +1
1. Pick two points anywhere on the line.
2. Count how many units you have to “rise” to get from the 1st point to the 2nd point.
+ 3
+ 3
3. Count how many units you have to “run” to get to the 2nd point.
Rise +3
4. The slope/rate of change is the rise divided by the run. +3
Run

10. Now it’s your turn, complete Finding Slope/Rate of Change from graphs.

11. Finding Slope /Rate of Change from a TABLE
1. Find the change in the y values. x y -3 4 2 3 6 -2 9 -4
2. Find the change in the x values. +3 -2
3. The slope/rate of change is the change in y divided by the change in x. -2 +3 +3 -2 +3 -2

12. Now it’s your turn, complete Finding Slope/Rate of Change from tables.

13. Finding Slope /Rate of Change when given 2 POINTS.
What is “m” the slope of the line that contains the points (-2, 6) and ( -6, 7)?
Let’s explore 2 methods!

14. Finding Slope /Rate of Change when given 2 POINTS.
Method 1: Using the Slope formula
m =

15. Finding Slope /Rate of Change when given 2 POINTS.
Method 1: Slope formula
m =
Label the points (x1,y1) and (x2,y2).
(-2, 6) and ( -6, 7) x1 y1 x2 y2
2. Plug in to the formula and solve. 7 6
m = -6 -2

16. Finding Slope /Rate of Change when given 2 POINTS.
Method 2: Graph the points and use rise/run.
(-2, 6) and ( -6, 7) -1 +4
Rise -1
Run 4

17. Now it’s your turn, complete Finding Slope/Rate of Change from given points.