Question

The equation of line fis - 3y + 4x = 9 write the equation of a line that is parallel to line and passes through the point (- 12, 6)

Answer 1

`y = - 4x - 42`

Explanation:

The equation of the line that is parallel to the line we are trying to find is

`- 3y + 4x = 9 \\ or \\ - 3y = - 4x + 9 \:(standard form) \\ \\therefore \: the \: slope \: of \: the \: line \\ \: is \: - 4`

We can recall that when two lines are parallel it means that they have the same slope. Therefore the slope of the line we are trying to find is also -4. We now know that:

`y = 6 \: \: \: x = - 12 \: \: \: slope = - 4`

Therefore the equation of the line is:

`y = mx + c \\ 6= ( - 4)( - 12) + c \\ 6 = 48 + c \\ 6 - 48 = c \\ - 42 = c`

`y = mx + c \\ y = - 4x - 42`