Find the Slope of a Line from its Graph

Math 102 2.3 "Determining the Equation of a Line" Objectives: * Find the slope of a line. * Solve application problems involving the slope of a line....
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Math 102 2.3 "Determining the Equation of a Line"

Objectives: * Find the slope of a line. * Solve application problems involving the slope of a line. * Write the equation of a line. The concept of slope has many applications. For example, architects use slope when designing ramps and determining the pitch of roofs. Truckers must be aware of the slope, or grade of a road. De…nitions: Ratios and Rates a A ratio is a comparison of two numbers using a quotient. If a and b are two numbers, the ratio of a to b is b Ratios that are used to compare quantities with di¤erent units are called rates.

Find the Slope of a Line from its Graph De…nition: Slope of a Line The slope of a line (m) is a ratio that compares the vertical change to the corresponding horizontal change as we move along the line from one point to another.

Example 1: (Finding the slope of a line from its graph) Find the slope of the line graphed below.

y -2

2

4

6

x

-5

Find the Slope of a Line given Two Points De…nition: Slope of a Line The slope of a line passing through points (x1 ; y1 ) and (x2 ; y2 ) is

Example 2: (Finding the slope of a line given two points) Find the slope of the line that passes through the given points. a) (3; 1) ; ( 6; 2)

b) ( 3; 6) ; (4; 8)

Page: 1

Notes by Bibiana Lopez

College Algebra by Kaufmann and Schwitters

2.3

Find the Slope of Horizontal and Vertical Lines Example 3: (Finding the slope of horizontal and vertical lines) Find the slope of the following lines. a) x =

3

b) y = 4

y

-4

y 4

4

2

2

-2

2

4

-2

-4

x

-2

2

4

x

-2

-4

-4

Slopes of Horizontal and Vertical Lines: Horizontal lines have a slope of Vertical lines have

Types of Slopes:

y

y

y

x

y

x

x

Positive Slope

Negative Slope

Zero Slope

m>0

m

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