Question

(3 -1) y=1/3x-3 write an equation of the line that passes through the given point and is parallel to the given line

Answer 1

`y = 1/3x-2`

Explanation:

General line equation:

`(y-y_(1))/(x-x_(1)) = (y_(2)-y_(1))/(x_(2)-x_(1))\\`

Or

`y = a.x + b\\a = (y_(2)-y_(1))/(x_(2)-x_(1))\\b = y_(1) - a.x_(1)`

where a is the slope and b is vertical displacement.

For a line to be parallel to another, they both have to have the same slope, therefor, the parallel line's slope is 1/3.

By substituting the given point and a = 1/3 in above equation for b, b is equal to -2. Therefore,

`y = 1/3x - 2`