1. Find The Equation Of The Line FTEOTL in Standard Form

2. 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

3. In case you forgot y - y1 = m ( x - x1 ) y = m x + b Ax + By = C
perpendicular lines have slopes that are negative recipricals of each other.
Parallel lines have slopes that are equal

4. 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

5. FTEOTL where m = and b = -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
Put in to standard form
first eliminate the fractions by multiply through by the LCD
Put into standard form
2y = 3x - 4
3x - 2y = 4

6. FTEOTL through the points (4,2) , (-2, -2)
First find the slope using the slope from two points formula
Plug in the values
Using the slope and one of the points in the point slope formula we get
Simplify
Put into standard form first eliminating the fractions
3y - 6 = 2x - 8
2x - 3y = 2

7. FTEOTL Perpendicular to 2x - 3y = 8 through the point ( 2, 1 )
Perpendicular means the slopes are negative inverses of each other
So mPerpendicular =
Using this slope, and the point given we get
Simplifying we get
Put into Standard form we get 2y - 2 = -3x + 6
3x + 2y = 8

8. FTEOTL Parallel to 2x - 3y = 9 Through the point 4, 3
Parallel means has the same slope