Rate of Change
ACT
Algebra II
2014
Bell Ringer
• What does the m determine in the
linear equation:
y=mx + b
Slope tree
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What is “Rate of Change”?
Mathematically Speaking…
Rate of Change is:
• a RATIO that compares
vertical change to
horizontal change
• a COMPARISON of two
different measures of
change
• a DIVISION of “rise” over
“run”
A ratio that compares the change in the
dependent (output) variable to the change in
the independent (input) variable.
Not lots of notes…just
The numerical value
for
a rate of change
GOOD notes!
between two values is found using two
points on the graph , and dividing the change
in y (dependent) values by the change in x
(independent) values.
Different Representations
•
•
•
•
Rate of Change Formula
Rise/Run on a Graph
Rate of Change in a linear equation
Change in a Table of Values
Rate of Change on a Graph
Rate of Change is a ratio of
the vertical change (rise) to
the horizontal change (run).
Ratio:
+3
-4
+2
-6
Rise: Vertical Change
Run: Horizontal Change
Up: Positive
Right: Positive
Down: Negative
Left: Negative
Rate of Change Between 2 Points
Rate of Change is a ratio of the vertical change (
the horizontal change (
).
) to
Ratio:
(0, 1)
(-3, -1)
(0, 1)
(3, 3)
(-3, -1)
On a line, the rate of change is CONSTANT, no matter which points you use.
On a curve, the rate of change will VARY depending on the points.
Rate of Change from
a Linear Equation
+3
+2
Rate of Change from
a Table of Linear Values
+3
+3
+2
-4
+2
-6
Write a ratio of the
change in the y-values to
the change in the x-values.
Linear Functions have a
CONSTANT RATE OF CHANGE
WHY??
Rate of Change from
a Table of Non-Linear Values
Rate of change between (-2,4) and (-1,1)
Rate of change between (2,4) and (1,1)
+1
“run”
-3
“rise”
+1
“run”
+3
“rise”
Write a ratio of the
change in the y-values to
the change in the x-values.
Non-Linear Functions have a
VARIABLE RATE OF CHANGE
WHY???
Variable or Constant Rate of Change?
Variable or Constant Rate of Change?
Variable or Constant Rate of Change?
homework
• Rate of Change worksheet,
due tomorrow