12-5 Slope

Course 2

Warm Up

Problem of the Day

Lesson Presentation

Learn to determine the slope of a line and to graph a line, given one point, the

y-intercept, and the slope.

Course 2

12-5 Slope

Vocabulary

slope

y-intercept

slope-intercept form

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Course 2

12-5 Slope

The slope of a line is a measure of its steepness and is the ratio of rise to run:

y

The y-coordinate of the point where a line crosses the y-axis is called the y-intercept.

x

Run

Rise

y-intercept

Course 2

12-5 Slope

A. Give the slope and y-intercept of the line.

Additional Example 1A: Identifying Slope and

y-intercept of a line

The rise is 3. The run is 3.

The y-intercept is –4.

slope = rise run

= 3 3

= 1

3

3

y-intercept

Course 2

12-5 Slope

Additional Example 1B: Identifying the Slope and

y-intercept of a Line

B. Give the slope and y-intercept of the line.

The rise is 0. The run is 2.

The y-intercept is –1.

slope = rise run

= 0 2

= 0

Course 2

12-5 Slope

y-intercept

2

Try This: Example 1A

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A. Give the slope and y-intercept of the line.

The rise is 0. The run is –8.

The y-intercept is –3.

slope = rise run

= 0 –8

= 0

Course 2

12-5 Slope

(4, –3)

–8

(–4, –3)

y-intercept

Try This: Example 1B

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B. Give the slope and y-intercept of the line.

Course 2

12-5 Slope

(0, –4)

y-intercept

(–2, 4)

8

–4 The rise is 8. The run is –4.

The y-intercept is 0.

slope = rise run

= 8 –4

= –2

A linear equation with the variable y isolated on the left-hand side of the equation is in slope-intercept form.

Course 2

12-5 Slope

y = mx + b

Slope y-intercept

Give the slope and y-intercept of each line, given the equation.

Additional Example 2: Identifying Slope and

y-intercept in a Linear Equation

A. y = 3x – 1 y = 3x – 1

The slope is 3. The y-intercept is –1.

B. 1 2 x + 2 y =

1 2

x + 2 y =

The slope is The y-intercept is 2.

1 2 .

Course 2

12-5 Slope

Try This: Example 2

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Give the slope and y-intercept of each line, given the equation.

A. y = 4x – 4 y = 4x – 4

The slope is 4. The y-intercept is –4.

B. 1 3 x + 3 y =

1 3

x + 3 y =

The slope is The y-intercept is 3.

1 3 .

Course 2

12-5 Slope

When you know the slope and any one point on a line, you can graph the line.

Course 2

12-5 Slope

Graph each line, given the equation.

Additional Example 3: Graphing Linear Equations

Using Slope and y-intercept

A. y = –2x + 1

y = –2x + 1

The slope is –2 or

2 –1

The y-intercept is 1. From point (0, 1) move 2 units up (rise) and 1 unit left (run) to find another point on the line. Draw a line to connect the points

(–1, 3)

Course 2

12-5 Slope

Additional Example 3B: Graphing Linear Equations

Using Slope and y-intercept

Graph the line, given the equation.

B. y = 3

y = 0x + 3

The slope is 0. The y- intercept is 3.

Locate the point (0, 3). When the slope is zero the line is horizontal. Draw a horizontal line through point (0, 3).

Course 2

12-5 Slope

(0, 3)

Try This: Example 3A

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Graph the line, given the equation.

A. y = x – 4

y = 1x – 4

The slope is 1. The y-intercept is –4.

From point (0, –4) move 1 unit up (rise) and 1 unit right (run) to find another point on the line. Draw a line to connect the points

Course 2

12-5 Slope

(0, –4)

(1, –3)

Try This: Example 3B

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Graph the line, given the equation.

B. y = –1

y = 0x – 1

The slope is 0. The y- intercept is –1.

Locate the point (0, –1). When the slope is zero the line is horizontal. Draw a horizontal line through point (0, –1).

Course 2

12-5 Slope

(0, –1) (–3, –1)

Lesson Quiz: Part 1

Tell the slope and y-intercept of each line, given the equation.

1. y = x – 5

2. y =

3. y = –2x + 7

3 4

1; –5

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–2; 7

3 4

x ; 0

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12-5 Slope

Lesson Quiz: Part 2

4. Graph the line, given the equation y =

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1 2 x – 2.

Course 2

12-5 Slope