2. Graphs, Linear Equations, and Functions
Chapter 4
Graphs, Linear Equations, and Functions

3. 4.2
Slope of a Line

4. 4.2 Slope of a Line Objectives
Find the slope of a line, given two points on the line.
Find the slope of a line, given an equation of the line.
Graph a line, given its slope and a point on the line.
Use slopes to determine whether two lines are parallel, perpendicular, or neither.
Solve problems involving average rate of change.
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5. Find the Slope of a Line Given Two Points on the Line
One of the important properties of a line is the rate at which it is increasing or decreasing. The slope is the ratio of vertical change, or rise, to horizontal change, or run.
As we move from P1 to P2: P1
4 ft P2
12 ft
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6. Find the Slope of a Line Given Two Points on the Line
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7. Finding the Slope of a Line
Find the slope of the line containing the points (–3, 1) and (3, 3).
Rise = 3 – 1 = 2
Run = 3 – (–3) = 6
There is a rise of 1 unit for a run of 3 units.
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8. Find the Slope of a Line given Two Points on the Line
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9. Find the Slope of a Line Given the Equation of the Line
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10. Finding the Slope of Horizontal and Vertical Lines
4.2 Slope of a Line
Finding the Slope of Horizontal and Vertical Lines
Find the slope of the line containing the points (–3, 2) and (4, 2).
Find the slope of the line containing the points (1, 3) and (1, –2).
Since the slope is 0, this is a horizontal line.
Since the slope is undefined, this is a vertical line.
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11. Finding the Slope from an Equation
4.2 Slope of a Line
Finding the Slope from an Equation
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12. Using the Slope and a Point to Graph a Line
4.2 Slope of a Line
Using the Slope and a Point to Graph a Line
Locate the point P(–5, 5). P
Down 2
From the slope formula: R
Right 3
So, move down 2 units and then 3 units to the right to the point R(–2, 3).
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13. Orientation of a Line in the Plane
4.2 Slope of a Line
Orientation of a Line in the Plane
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14. Slopes of Parallel and Perpendicular Lines
4.2 Slope of a Line
Slopes of Parallel and Perpendicular Lines
Since parallel lines have the same slope, any line parallel to this line will have slope –2.
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15. Slopes of Parallel and Perpendicular Lines
4.2 Slope of a Line
Slopes of Parallel and Perpendicular Lines
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16. Slopes of Parallel and Perpendicular Lines
4.2 Slope of a Line
Slopes of Parallel and Perpendicular Lines
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17. Interpreting Slope as Average Rate of Change
4.2 Slope of a Line
Interpreting Slope as Average Rate of Change
Cindy purchased a new care in 2001 for $18,000. In 2006, the car had a value of $ At what rate is the car’s value changing with respect to time?
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