![Page 1: Rate of Change SLOP E AKA. Types of Slopes Negative Slope Lines that have negative slopes “slant downhill” as viewed from left to right](https://reader036.vdocuments.mx/reader036/viewer/2022062504/5a4d1b367f8b9ab05999d1e7/html5/thumbnails/1.jpg)
Rate of Change
SLOPE
AKA
![Page 2: Rate of Change SLOP E AKA. Types of Slopes Negative Slope Lines that have negative slopes “slant downhill” as viewed from left to right](https://reader036.vdocuments.mx/reader036/viewer/2022062504/5a4d1b367f8b9ab05999d1e7/html5/thumbnails/2.jpg)
Types of
Slopes
![Page 3: Rate of Change SLOP E AKA. Types of Slopes Negative Slope Lines that have negative slopes “slant downhill” as viewed from left to right](https://reader036.vdocuments.mx/reader036/viewer/2022062504/5a4d1b367f8b9ab05999d1e7/html5/thumbnails/3.jpg)
Negative SlopeLines that have negative slopes “slant downhill” as viewed from left to right.
![Page 4: Rate of Change SLOP E AKA. Types of Slopes Negative Slope Lines that have negative slopes “slant downhill” as viewed from left to right](https://reader036.vdocuments.mx/reader036/viewer/2022062504/5a4d1b367f8b9ab05999d1e7/html5/thumbnails/4.jpg)
Zero SlopeHorizontal lines have Zero “slant” or SLOPE.
![Page 5: Rate of Change SLOP E AKA. Types of Slopes Negative Slope Lines that have negative slopes “slant downhill” as viewed from left to right](https://reader036.vdocuments.mx/reader036/viewer/2022062504/5a4d1b367f8b9ab05999d1e7/html5/thumbnails/5.jpg)
Positive SlopeLines that have positive slopes “slant uphill” as viewed from left to right.
![Page 6: Rate of Change SLOP E AKA. Types of Slopes Negative Slope Lines that have negative slopes “slant downhill” as viewed from left to right](https://reader036.vdocuments.mx/reader036/viewer/2022062504/5a4d1b367f8b9ab05999d1e7/html5/thumbnails/6.jpg)
No SlopeVertical lines have NO SLOPE or an Undefined Slope
![Page 7: Rate of Change SLOP E AKA. Types of Slopes Negative Slope Lines that have negative slopes “slant downhill” as viewed from left to right](https://reader036.vdocuments.mx/reader036/viewer/2022062504/5a4d1b367f8b9ab05999d1e7/html5/thumbnails/7.jpg)
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.
2 1
2 1
y yx x
Let’s Explore!
![Page 8: Rate of Change SLOP E AKA. Types of Slopes Negative Slope Lines that have negative slopes “slant downhill” as viewed from left to right](https://reader036.vdocuments.mx/reader036/viewer/2022062504/5a4d1b367f8b9ab05999d1e7/html5/thumbnails/8.jpg)
Slope AKA Rate of Change is the measurement of steepness
of a straight line.
x
y
![Page 9: Rate of Change SLOP E AKA. Types of Slopes Negative Slope Lines that have negative slopes “slant downhill” as viewed from left to right](https://reader036.vdocuments.mx/reader036/viewer/2022062504/5a4d1b367f8b9ab05999d1e7/html5/thumbnails/9.jpg)
Finding Slope /Rate of Change on a GRAPH
x
y
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. Count how many units you have to “run” to get to the 2nd point.
+ 3
4. The slope/rate of change is the rise divided by the run.
Rise
Run
+3 +3
Rate of change or slope is +1
![Page 10: Rate of Change SLOP E AKA. Types of Slopes Negative Slope Lines that have negative slopes “slant downhill” as viewed from left to right](https://reader036.vdocuments.mx/reader036/viewer/2022062504/5a4d1b367f8b9ab05999d1e7/html5/thumbnails/10.jpg)
Now it’s your turn, complete Finding
Slope/Rate of Change from
graphs.
![Page 11: Rate of Change SLOP E AKA. Types of Slopes Negative Slope Lines that have negative slopes “slant downhill” as viewed from left to right](https://reader036.vdocuments.mx/reader036/viewer/2022062504/5a4d1b367f8b9ab05999d1e7/html5/thumbnails/11.jpg)
Finding Slope /Rate of Change from a TABLEx y-3 40 23 06 -29 -4
1. Find the change in the y values.
-2
-2
-2
-2
2. Find the change in the x values.
+3
+3
+3
+3
3. The slope/rate of change is the change in y divided by the change in x.
23m
![Page 12: Rate of Change SLOP E AKA. Types of Slopes Negative Slope Lines that have negative slopes “slant downhill” as viewed from left to right](https://reader036.vdocuments.mx/reader036/viewer/2022062504/5a4d1b367f8b9ab05999d1e7/html5/thumbnails/12.jpg)
Now it’s your turn, complete Finding
Slope/Rate of Change from tables.
![Page 13: Rate of Change SLOP E AKA. Types of Slopes Negative Slope Lines that have negative slopes “slant downhill” as viewed from left to right](https://reader036.vdocuments.mx/reader036/viewer/2022062504/5a4d1b367f8b9ab05999d1e7/html5/thumbnails/13.jpg)
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!
![Page 14: Rate of Change SLOP E AKA. Types of Slopes Negative Slope Lines that have negative slopes “slant downhill” as viewed from left to right](https://reader036.vdocuments.mx/reader036/viewer/2022062504/5a4d1b367f8b9ab05999d1e7/html5/thumbnails/14.jpg)
Finding Slope /Rate of Change when given 2 POINTS.
Method 1: Using the Slope formula
2 1
2 1
y yx xm =
![Page 15: Rate of Change SLOP E AKA. Types of Slopes Negative Slope Lines that have negative slopes “slant downhill” as viewed from left to right](https://reader036.vdocuments.mx/reader036/viewer/2022062504/5a4d1b367f8b9ab05999d1e7/html5/thumbnails/15.jpg)
Finding Slope /Rate of Change when given 2 POINTS.
Method 1: Slope formula
2 1
2 1
y yx x
m =
(-2, 6) and ( -6, 7)1. Label the points (x1,y1) and (x2,y2).
x1 x2y1 y2
2. Plug in to the formula and solve.
m =
2 1
2 1
y yx x7 6
-6 -2 14m
![Page 16: Rate of Change SLOP E AKA. Types of Slopes Negative Slope Lines that have negative slopes “slant downhill” as viewed from left to right](https://reader036.vdocuments.mx/reader036/viewer/2022062504/5a4d1b367f8b9ab05999d1e7/html5/thumbnails/16.jpg)
Finding Slope /Rate of Change when given 2 POINTS.
Method 2: Graph the points and use rise/run. (-2, 6) and ( -6, 7)
x
y
-1+4
RiseRun 4
-1
14m
![Page 17: Rate of Change SLOP E AKA. Types of Slopes Negative Slope Lines that have negative slopes “slant downhill” as viewed from left to right](https://reader036.vdocuments.mx/reader036/viewer/2022062504/5a4d1b367f8b9ab05999d1e7/html5/thumbnails/17.jpg)
Now it’s your turn, complete Finding
Slope/Rate of Change from given
points.