Math 102 2.3 "Determining the Equation of a Line"

Objectives: * Find the slope of a line determined by two points. * Write the equation of a line, given the slope and a point contained in the line. * Write the equation of a line, given two points contained in the line. * Write the equation of a line parallel or perpendicular to another line and containing a speci…ed point. * Solve application problems involving the slope of a line.

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"

If P1 and P2 are any two di¤erent points on a line, P1 with coordinates (x1 ; y1 ) and P2 with coordinates (x2 ; y2 ) ; then the slope of the line (denoted by m) is

where x1 6= x2 :

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 a horizontal line) 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 Positive Slope m>0

y

x Negative Slope

x Zero Slope

m