1.1 Lines in a Plane

• Finding the slope of a line• Using Point-Slope form of the equation of a line• Using Slope-Intercept form of the equation of a

line• Using General (Standard) form of the equation of

a line• Finding the equations of parallel and

perpendicular lines

The slope m of a line through the points ( , ) ( , )x y and x y is

my y

x x

1 1 2 2

2 1

2 1

Example 1

• Find the slope of the line passing through each pair of points

(-2,0) and (3,1)

Find the slope of the line containing (-1,2) and (2,2)

Find the slope of the line containing (0,4) and (1,-1)

Student Example

Find the slope of a line containing the points (-4,6) and (5,-2)

Lines may take 4 different forms:

Positive Slope Negative Slope

Slope of Zero Undefined Slope

The Point-Slope Form of a LineThe line passing through the point and has a slope of m can be written

y y m x x 1 1( )

( , )x y1 1

Example 2

Find an equation of a line that passes through the point (1,-2) and has a slope of 3.

y y m x x 1 1( )

Slope-Intercept Form

y=mx+b where m is the slope and (0,b) is the y-intercept

Give the equation of a line passing through the point (1,-2) and has a slope of 3.

Student Example

Find an equation of a line that passes through the point (2,-4) and has a slope of –2.

a. Give the equation in point-slope form

b. Give the equation in slope-intercept form

Example 3

During 2000, Nike’s net sales were $9 billion, and in 2001 net sales were $9.5 billion. Write a linear equation giving the net sales y in terms of the year x. Then use the equation to predict the net sales for 2002.

Example 4

Determine the slope and the y-intercept of each linear equation.

a. x+y=2 b. y=2

Example 5

The graphs of y=-x-1 and y=-10x-1 are shown on p. 8. What is different about the graphing calculator that would make both graphs appear the same?

Example 6

Find the slope-intercept form of the equation of the line that passes through the point (2,-1) and is parallel to the line 2x-3y=5.

*Hint – Parallel lines have the same slope

Student Example

Find the slope-intercept form of the equation of the line that passes through the point (-2,4) and is parallel to the line x-2y=5.

Example 7

Find the slope-intercept form of a line that passes through the point (2,-1) and is perpendicular to the line 2x-3y=5

*Hint – Perpendicular lines have opposite reciprocal slope

Student Example

Find the slope-intercept form of the equation of the line that passes through the point (-2,4) and is perpendicular to the line x-2y=5.

Example 8

Graph the lines y=x+1 and y=-x+3 on your graphing calculator. If these lines are suppose to be perpendicular, why don’t they appear as such on your calculator screen?

p. 11-12, 1st problem in each section

p. 13-14 #65, 69, 71, 75-79