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Contents Lesson 5-1Slope

Lesson 1 Contents Example 1Positive Slope Example 2Negative Slope Example 3Zero Slope Example 4Undefined Slope Example 5Find Coordinates Given Slope Example 6Find a Rate of Change

Example 1-1a Find the slope of the line that passes through (–3, 2) and (5, 5). Let and Substitute.

Example 1-1b Simplify. Answer:The slope is

Example 1-1c Find the slope of the line that passes through (4, 5) and (7, 6). Answer:

Example 1-2a Find the slope of the line that passes through (–3, –4) and (–2, –8). Substitute. Let and

Example 1-2b Answer:The slope is –4. Simplify.

Example 1-2c Find the slope of the line that passes through (–3, –5) and (–2, –7). Answer: –2

Let and Example 1-3a Find the slope of the line that passes through (–3, 4) and (4, 4). Substitute.

Example 1-3b Answer:The slope is 0. Simplify.

Example 1-3c Find the slope of the line that passes through (–3, –1) and (5, –1). Answer: 0

Let and Example 1-4a Find the slope of the line that passes through (–2, –4) and (–2, 3). Answer:Since division by zero is undefined, the slope is undefined.

Example 1-4b Find the slope of the line that passes through (5, –1) and (5, –3). Answer:undefined

Example 1-5a Find the value of r so that the line through ( 6, 3 ) and ( r, 2 ) has a slope of Slope formula Substitute. Subtract.

Example 1-5b Find the cross products. Simplify. Add 6 to each side. Answer:Simplify.

Example 1-5c Find the value of p so that the line through ( p, 4 ) and ( 3, –1 ) has a slope of Answer: –5

Example 1-6a Travel The graph to the right shows the number of U.S. passports issued in 1991, 1995, and Find the rates of change for and Use the formula for slope. millions of passports years

Example 1-6b : Substitute. Simplify. Answer: The number of passports issued increased by 1.9 million in a 4-year period for a rate of change of 475,000 per year.

Example 1-6c : Substitute. Simplify. Answer: Over this 4-year period, the number of U.S. passports issued increased by 1.4 million for a rate of change of 350,000 per year.

Example 1-6d Explain the meaning of slope in each case. Answer: For , on average, 475,000 more passports were issued each year than the last. For , on average, 350,000 more passports were issued each year than the last.

Example 1-6e How are the different rates of change shown on the graph? Answer: There is a greater rate of change from than from Therefore, the section of the graph for has a steeper slope.

Example 1-6f Airlines The graph shows the number of airplane departures in the United States in recent years. a.Find the rates of change for and Answer:240,000 per year; 180,000 per year

Example 1-6g b.Explain the meaning of the slope in each case. Answer:For , the number of airplane departures increased by about 240,000 flights each year. For , the number of airplane departures increased by about 180,000 flights each year.

Example 1-6h c.How are the different rates of change shown on the graph? Answer:There is a greater vertical change for than for Therefore, the section of the graph for has a steeper slope.

End of Lesson 1

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