1. Finding Slope and Rate of Change
Section 2.2
2.2: Slope and Rate of Change
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2. 2.2: Slope and Rate of Change
Definitions
Linear equation: An equation whose graph is a line
Slope is a non-vertical line of the vertical change to the horizontal change between two points of a line
Y-intercept is where the line crosses the y-axis
2.2: Slope and Rate of Change
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3. 2.2: Slope and Rate of Change
Slope Equation
Slope equation:
Rewrite it as:
Rise: The number of points up (vertically) from the previous point
Run: The number of points sideways (horizontally) from the rise
2.2: Slope and Rate of Change
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4. 2.2: Slope and Rate of Change
Types of Slope
Positive
Slope
Negative
Slope
2.2: Slope and Rate of Change
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5. 2.2: Slope and Rate of Change
Types of Slope
Zero
Slope
Horizontal Line
2.2: Slope and Rate of Change
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6. 2.2: Slope and Rate of Change
Types of Slope
No Slope/
Undefined
Vertical Line
2.2: Slope and Rate of Change
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7. 2.2: Slope and Rate of Change
Zero versus Undefined
2.2: Slope and Rate of Change
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8. 2.2: Slope and Rate of Change
Undefined Slope
2.2: Slope and Rate of Change
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9. 2.2: Slope and Rate of Change
Steps
Find the change of Y and change of X of two of the points
Determine the ratios for both
Simplify the ratio
Repeat the process for two other points
Check answer
2.2: Slope and Rate of Change
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10. Create a t-chart & solve for slope
Example 1
What is the slope of these two points, (–1, 3) and (2, –2)? Will it rise, fall, horizontal, or vertical?
Create a t-chart & solve for slope x y –1 3 2 –2
–1 – (2) = –3
3 – (–2) = 5
2.2: Slope and Rate of Change
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11. 2.2: Slope and Rate of Change
Example 1
What is the slope of these two points, (–1, 3) and (2, –2)? Will it rise, fall, horizontal, or vertical? –2 3 2 –1
2.2: Slope and Rate of Change
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12. 2.2: Slope and Rate of Change
Your Turn
What is the slope of this table? Will it rise, fall, horizontal, or vertical? +2 –1 +2 –1 +2 –1 x –2 2 4
f(x) 1 –1
2.2: Slope and Rate of Change
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13. 2.2: Slope and Rate of Change
Example 2
What is the slope of this table? Will it rise, fall, horizontal, or vertical? +1 +2 +1 +4 +1 +8 x 2 3 4 5
f(x) 8 16
2.2: Slope and Rate of Change
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14. 2.2: Slope and Rate of Change
Your Turn
What is the slope of these two points, (1, –5) and (1, 0)? Will it rise, fall, horizontal, or vertical?
2.2: Slope and Rate of Change
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15. 2.2: Slope and Rate of Change
Example 3
What is the slope of these two points, f(2) = 2 and f(6) = 8? Will it rise, fall, horizontal, or vertical?
2.2: Slope and Rate of Change
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16. 2.2: Slope and Rate of Change
Example 4
What is the slope of these two points, f(a) = 3 and f(–2a) = 7?
2.2: Slope and Rate of Change
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17. 2.2: Slope and Rate of Change
Your Turn
What is the slope of these two points, f(2) = 8 and f(6) = 8? Will it rise, fall, horizontal, or vertical?
2.2: Slope and Rate of Change
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18. 2.2: Slope and Rate of Change
Assignment
Page 86
3-17 odd, odd
2.2: Slope and Rate of Change
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