slopes and equations of lines advanced geometry parallel and perpendicular lines lesson 2
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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.