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