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Distance, Slope, & Linear Equations
Distance, Slope, & Linear Equations
Distance Formula 221
221 yyxxd
Distance, Slope, & Linear Equations
Distance Formula 221
221 yyxxd
EXAMPLE : Find the distance between ( 3 , 1 ) and ( -2 , 4 )
Distance, Slope, & Linear Equations
Distance Formula 221
221 yyxxd
EXAMPLE : Find the distance between ( 3 , 1 ) and ( -2 , 4 )
34925
35
4123
22
22
d
d
d
x1 y1 x2 y2
Distance, Slope, & Linear Equations
axmby
bmxy
Point – Slope Form
Slope – Intercept Form
Distance, Slope, & Linear Equations
axmby
bmxy
Point – Slope Form
Slope – Intercept Form
EXAMPLE # 1 : Find the equation of the line with m = -3 thru the point ( - 2 , 4 )
Distance, Slope, & Linear Equations
axmby
bmxy
Point – Slope Form
Slope – Intercept Form
EXAMPLE # 1 : Find the equation of the line with m = -3 thru the point ( - 2 , 4 )
234
)2(34
xy
xy
axmby
Distance, Slope, & Linear Equations
axmby
bmxy
Point – Slope Form
Slope – Intercept Form
EXAMPLE # 2 : Find the equation of the line with m = -1/2 thru the point ( 0 , -3 )
Distance, Slope, & Linear Equations
axmby
bmxy
Point – Slope Form
Slope – Intercept Form
EXAMPLE # 2 : Find the equation of the line with m = -1/2 thru the point ( 0 , -3 )
32
1
xy
bmxy
Distance, Slope, & Linear Equations
axmby
bmxy
Point – Slope Form
Slope – Intercept Form
EXAMPLE # 3 : What is the slope and y – intercept for
44
13 xy
Distance, Slope, & Linear Equations
axmby
bmxy
Point – Slope Form
Slope – Intercept Form
EXAMPLE # 3 : What is the slope and y – intercept for
44
13 xy
4
1m
Distance, Slope, & Linear Equations
bxmay
bmxy
Point – Slope Form
Slope – Intercept Form
EXAMPLE # 3 : What is the slope and y – intercept for
44
13 xy
4
1m
2
33
13
44
13
404
13
y
y
y
y
y – intercept, where x = 0
Distance, Slope, & Linear Equations
axmby
bmxy
Point – Slope Form
Slope – Intercept Form
EXAMPLE # 4 : What is the slope and y – intercept for
632 yx
Distance, Slope, & Linear Equations
axmby
bmxy
Point – Slope Form
Slope – Intercept Form
EXAMPLE # 4 : What is the slope and y – intercept for
23
23
6
3
2
3
3
623
632
xy
xy
xy
yx
Solve for “y”
Distance, Slope, & Linear Equations
bxmay
bmxy
Point – Slope Form
Slope – Intercept Form
EXAMPLE # 4 : What is the slope and y – intercept for
23
23
6
3
2
3
3
623
632
xy
xy
xy
yx
2,03
2
b
m
m b
Distance, Slope, & Linear Equations
Parallel & Perpendicular Lines
Parallel lines have the SAME slope m1 = m2
Perpendicular lines are reciprocal and opposite signs
Distance, Slope, & Linear Equations
Parallel & Perpendicular Lines
Parallel lines have the SAME slope m1 = m2
Perpendicular lines are reciprocal and opposite signs
EXAMPLE : Find the equation of the line parallel to
thru ( 2 , -1 ).
52 xy
Distance, Slope, & Linear Equations
Parallel & Perpendicular Lines
Parallel lines have the SAME slope m1 = m2
Perpendicular lines are reciprocal and opposite signs
EXAMPLE : Find the equation of the line parallel to
thru ( 2 , -1 ).
52 xy
axmby
m
2m
** use point – slope form
Distance, Slope, & Linear Equations
Parallel & Perpendicular Lines
Parallel lines have the SAME slope m1 = m2
Perpendicular lines are reciprocal and opposite signs
EXAMPLE : Find the equation of the line parallel to
thru ( 2 , -1 ).
52 xy
221
221
2
xy
xy
axmby
mm
Distance, Slope, & Linear Equations
Parallel & Perpendicular Lines
Parallel lines have the SAME slope m1 = m2
Perpendicular lines are reciprocal and opposite signs
EXAMPLE # 2 : Are the given equations parallel, perpendicular, or neither ?
54 and 64 yxyx
Distance, Slope, & Linear Equations
Parallel & Perpendicular Lines
Parallel lines have the SAME slope m1 = m2
Perpendicular lines are reciprocal and opposite signs
EXAMPLE # 2 : Are the given equations parallel, perpendicular, or neither ?
2
3
4
1y
4
6
44
4
54 64
54 and 64
x
xy
xyxy
yxyx
Perpendicular–
Slopes are reciprocal and opposite signs
