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  • Warm Up Add or subtract. 1. 4 + (–6)2. –3 + 5 3. –7 – 74. 2 – (–1) –2 –14 2 3 5. Find the x- and y-intercepts of 2x – 5y = 20. x-int.: 10; y-int.: –4
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Slope Lesson 5.3

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Page 1: Warm Up Add or subtract. 1. 4 + (–6)2. –3 + 5 3. –7 – 74. 2 – (–1) –2 –14 2 3 5. Find the x- and y-intercepts of 2x – 5y = 20. x-int.: 10; y-int.: –4

Slope

Lesson 5.3

Page 2: Warm Up Add or subtract. 1. 4 + (–6)2. –3 + 5 3. –7 – 74. 2 – (–1) –2 –14 2 3 5. Find the x- and y-intercepts of 2x – 5y = 20. x-int.: 10; y-int.: –4

Objectives

• Graph linear functions, noting that the vertical change per unit of horizontal change is always the same and is called the slope of a line (AF 3.3)

• Fit a line to a plot and understand that the slope of the line equals the ratio of the quantities (AF 3.4)

Page 3: Warm Up Add or subtract. 1. 4 + (–6)2. –3 + 5 3. –7 – 74. 2 – (–1) –2 –14 2 3 5. Find the x- and y-intercepts of 2x – 5y = 20. x-int.: 10; y-int.: –4

• a nonvertical line is the ratio of the rise to the run between any two points on the line.

• Slope = “steepness” of a line.

run

rise

Slope –

Page 4: Warm Up Add or subtract. 1. 4 + (–6)2. –3 + 5 3. –7 – 74. 2 – (–1) –2 –14 2 3 5. Find the x- and y-intercepts of 2x – 5y = 20. x-int.: 10; y-int.: –4

Find the slope of the line.

Begin at one point and count vertically to find the rise.

Then count horizontally to the second point to find the run.

Run = 4

Rise =–2

Run = –4

Rise = 2

Riserun

Page 5: Warm Up Add or subtract. 1. 4 + (–6)2. –3 + 5 3. –7 – 74. 2 – (–1) –2 –14 2 3 5. Find the x- and y-intercepts of 2x – 5y = 20. x-int.: 10; y-int.: –4

Finding Slopes of Horizontal

and Vertical Lines A. B.

The slope is undefined. The slope is 0.

Page 6: Warm Up Add or subtract. 1. 4 + (–6)2. –3 + 5 3. –7 – 74. 2 – (–1) –2 –14 2 3 5. Find the x- and y-intercepts of 2x – 5y = 20. x-int.: 10; y-int.: –4

Real World Slope

Page 7: Warm Up Add or subtract. 1. 4 + (–6)2. –3 + 5 3. –7 – 74. 2 – (–1) –2 –14 2 3 5. Find the x- and y-intercepts of 2x – 5y = 20. x-int.: 10; y-int.: –4
Page 8: Warm Up Add or subtract. 1. 4 + (–6)2. –3 + 5 3. –7 – 74. 2 – (–1) –2 –14 2 3 5. Find the x- and y-intercepts of 2x – 5y = 20. x-int.: 10; y-int.: –4

Find the slope of the line

Page 9: Warm Up Add or subtract. 1. 4 + (–6)2. –3 + 5 3. –7 – 74. 2 – (–1) –2 –14 2 3 5. Find the x- and y-intercepts of 2x – 5y = 20. x-int.: 10; y-int.: –4

Find the slope of the line

Page 10: Warm Up Add or subtract. 1. 4 + (–6)2. –3 + 5 3. –7 – 74. 2 – (–1) –2 –14 2 3 5. Find the x- and y-intercepts of 2x – 5y = 20. x-int.: 10; y-int.: –4

How do you find the slope on the graph?

Page 11: Warm Up Add or subtract. 1. 4 + (–6)2. –3 + 5 3. –7 – 74. 2 – (–1) –2 –14 2 3 5. Find the x- and y-intercepts of 2x – 5y = 20. x-int.: 10; y-int.: –4

Kinds of Slopes

(It helps to remember how you would walk on these lines.)

Positive slope – walking up hill.

Negative slope – walking down a hill.

No slope – walking on level ground

http://www.animationlibrary.com/animation/25073/Green_choco/
Page 12: Warm Up Add or subtract. 1. 4 + (–6)2. –3 + 5 3. –7 – 74. 2 – (–1) –2 –14 2 3 5. Find the x- and y-intercepts of 2x – 5y = 20. x-int.: 10; y-int.: –4

Let’s practice- find the slope of the line.

2

1

4

3

13

21

)1(3

)1(2

Page 13: Warm Up Add or subtract. 1. 4 + (–6)2. –3 + 5 3. –7 – 74. 2 – (–1) –2 –14 2 3 5. Find the x- and y-intercepts of 2x – 5y = 20. x-int.: 10; y-int.: –4

Find a slope of two points

(2, 5) and (8, 1).(x1, y1) (x2, y2).

Use the slope formula.

Substitute (2, 5) for (x1, y1) and (8, 1) for (x2, y2).

Page 14: Warm Up Add or subtract. 1. 4 + (–6)2. –3 + 5 3. –7 – 74. 2 – (–1) –2 –14 2 3 5. Find the x- and y-intercepts of 2x – 5y = 20. x-int.: 10; y-int.: –4

Find a slope of two points

(5, –7) and (6, –4)(x1, y1) (x2, y2).

RiseRun

yx

5

6-7

-4+3

x y

+1

31

Page 15: Warm Up Add or subtract. 1. 4 + (–6)2. –3 + 5 3. –7 – 74. 2 – (–1) –2 –14 2 3 5. Find the x- and y-intercepts of 2x – 5y = 20. x-int.: 10; y-int.: –4

Find a slope of two points

(5, 3) and (–1, 4)(x1, y1) (x2, y2).

RiseRun

yx

5

-13

4+1

x y

-6

1-6

Page 16: Warm Up Add or subtract. 1. 4 + (–6)2. –3 + 5 3. –7 – 74. 2 – (–1) –2 –14 2 3 5. Find the x- and y-intercepts of 2x – 5y = 20. x-int.: 10; y-int.: –4

Find a slope of two points

(1, 3) and (–2, 1)(x1, y1) (x2, y2).

RiseRun

yx

1

-23

1-2

x y

-3

-2-3

23

Page 17: Warm Up Add or subtract. 1. 4 + (–6)2. –3 + 5 3. –7 – 74. 2 – (–1) –2 –14 2 3 5. Find the x- and y-intercepts of 2x – 5y = 20. x-int.: 10; y-int.: –4

And one last laugh…

Page 18: Warm Up Add or subtract. 1. 4 + (–6)2. –3 + 5 3. –7 – 74. 2 – (–1) –2 –14 2 3 5. Find the x- and y-intercepts of 2x – 5y = 20. x-int.: 10; y-int.: –4

Summary

• The constant rate of change of a nonvertical line is called the slope.

• If you know 2 different points on a line, you can use the slope formula to find the slope of the line

• If you know the equation of a line, you can also find the slope by using any two ordered-pair solutions

• Slope can be positive, negative, zero, and undefined

Page 19: Warm Up Add or subtract. 1. 4 + (–6)2. –3 + 5 3. –7 – 74. 2 – (–1) –2 –14 2 3 5. Find the x- and y-intercepts of 2x – 5y = 20. x-int.: 10; y-int.: –4

Lesson QuizFind the slope of each line.

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1. 2.

Page 20: Warm Up Add or subtract. 1. 4 + (–6)2. –3 + 5 3. –7 – 74. 2 – (–1) –2 –14 2 3 5. Find the x- and y-intercepts of 2x – 5y = 20. x-int.: 10; y-int.: –4

Lesson Quiz –part 23. Find the slope of the line that contains (5, 3) and (–1, 4).

4. Find the slope. Then tell what the slope represents.

A slope of 50 means that the speed of the bus is 50 mi/h.

50

5. Find the slope of the line given by x – 2y = 8.


Practice solving systems by graphing 1.)2.) 2x + 5y = –5 x + 3y = 3

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