Find The Equation Of The Line FTEOTL in Standard Form.
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Transcript of Find The Equation Of The Line FTEOTL in Standard Form.
Find The Equation Of The LineFTEOTL
in Standard Form
Things you need to know
Things used in finding the equation of a line
Point slope form of the equation
Slope intercept form of the equation
Standard form of the equation
Slope from two points
Definition of perpendicular
Definition of parallel
In case you forgot
y - y1 = m ( x - x1 )
y = m x + b
Ax + By = C2 1
2 1
y yx x
m
perpendicular lines have slopes that are negative recipricals of each other.Parallel lines have slopes that are equal
FTEOTL through 5,4 with a slope of 3
Since we have a point and a slope, the most efficient way to do this problem would be using the point slope form of the equation
y - y1 = m ( x - x1 )
Plug in the point and the slope
y - 4 = 3 ( x - 5 )
Simplify
y - 4 = 3x - 15
Put into standard form
3x - y = 11
FTEOTL where m = and b = -23
2
Since we have the slope and the y intercept the most efficient way of doing this problem would be to use the slope intercept form
y = mx + b Plug in the values we get
y x 3
22 Put in to standard form
first eliminate the fractions by multiply through by the LCD
2y = 3x - 4 Put into standard form
3x - 2y = 4
FTEOTL through the points(4,2) , (-2, -2)
First find the slope using the slope from two points formula
2 1
2 1
y yx x
m
Plug in
the values
2 2
2 4
4
6
2
3m
Using the slope and one of the points in the point slope formula we get
y x 22
34( ) Simplify y x 2
2
3
8
3
Put into standard form first eliminating the fractions3y - 6 = 2x - 82x - 3y = 2
FTEOTL Perpendicular to 2x - 3y = 8 through the point ( 2, 1 )Perpendicular means the slopes are negative inverses of each
other
originalmA
B
( )2
3
2
3So mPerpendicular =
12
3
3
2
Using this slope, and the point given we get
y x
13
22( ) Simplifying we get y x
1
3
23
Put into Standard form we get 2y - 2 = -3x + 63x + 2y = 8
FTEOTL Parallel to 2x - 3y = 9 Through the point 4, 3
Parallel means has the same slope