Finding Equation of a Line

There are many types of equations that can be asked, one example of each type will be presented.

(1) Finding Horizontal Lines

Example-
Determine the equation of a horizontal line passing through (6,5)
All horizontal lines take the form y = #, in this case y = 5

(2) Finding Vertical Lines

Example-
Determine the equation of a vertical line passing through (6,5)
All vertical lines take the form x = #, in this case x = 6

(3) Given Slope and y - intercept

Example-
Determine the equation of a line whoise slope = 2 and y -intercept = 6

Using
y = mx + b
m = 2 and b = 6

Therefore the equation is y = 2x + 6

(4) Given Slope and a Point

Example-
Determine the equation of a vertical line passing through (3,2) and has a slope of -2

Using
y = mx + b
m = -2, x = 3 and y= 2
(2) = (-2)(3)+ b we can find b
2 = -6 + b
8 = b

Therefore the equation (y = mx +b) is y = -2x + 8

(5) Given Two Points

Example-
Determine the equation of a vertical line passing through (2,3) and (-1,5)

The first step is to determine the slope