Slopes and Equations of Lines

Advanced GeometryParallel and Perpendicular Lines

Lesson 2

riserun

verticalslope

horizontal

**Slope can also be called a rate of change.

SlopePoint 1:

and Point 2:

1 1,x y

2 2,x y

2 1

2 1

y ym

x x

AB�������������� �Find the slope of each line.

, if A(-3, 7) and B(-1, -1)

Find the slope of each line.

Horizontal Line (flat) m = 0

Vertical Line(up and down)m = undefined

Special Cases

( 1,3) ( 2,3)and (3, 1) (3, 2)and

For one manufacturer of camping equipment, between 1995 and 2005 annual sales increased by $7.4 million per year. In 2005, the total sales were $85.9 million. If sales increase at the same rate, what will be the total sales in 2015?

Parallel and Perpendicular Slopes

•different signs•flip the fraction

Perpendicular lines have slopes that are

negativereciprocals.

Parallel lines have

exactly the same slope.

•same sign•same numbers in the same places

2 2

3 3and

2 3

3 2and

FG�������������� �

HJ�������������� �

Determine whether and are parallel, perpendicular, or neither. F(-2, -5), G(4, 7), H(0, 2), J(8, -2)

FG�������������� �

HJ�������������� �

Determine whether and are parallel, perpendicular, or neither. F(4, 2), G(6, -3), H(-1, 5), J(-3, 10)

FG�������������� �

HJ�������������� �

Determine whether and are parallel, perpendicular, or neither. F(1, -3), G(-2, -1), H(5, 0), J(6, 3)

Graph the line that contains Q(5, 1) and is parallel to with M(-2, 4)

and N(2, 1). MN�������������� �

Graph the line that contains A(0, 1) and is perpendicular to with X(-6, -2) and Y(0, -6).

XY�������������� �

Write an equation in slope-intercept form of the line with slope of -6 and y-intercept of (0, -2).

Equations of Lines

Slope-Intercept Form

y = mx + b

m: slope b: y-intercept

1 1( )y xmy x

3

5

Point-slope Form

Write an equation in point-slope form of the line whose slope is that contains (-10, 8).

Equations of Lines

m: slope 1 1, : a pointx y

Write an equation in slope-intercept form for a line containing (4, 9) and (-2, 0).

Write an equation in slope-intercept form for a line containing (1, 7) that is

perpendicular to the line y = 12

x + 1.