Answer:
[tex]y = - 4x - 42[/tex]
Step-by-step explanation:
The equation of the line that is parallel to the line we are trying to find is
[tex] - 3y + 4x = 9 \\ or \\ - 3y = - 4x + 9 \:(standard form) \\ \\therefore \: the \: slope \: of \: the \: line \\ \: is \: - 4[/tex]
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:
[tex]y = 6 \: \: \: x = - 12 \: \: \: slope = - 4[/tex]
Therefore the equation of the line is:
[tex]y = mx + c \\ 6= ( - 4)( - 12) + c \\ 6 = 48 + c \\ 6 - 48 = c \\ - 42 = c[/tex]
[tex]y = mx + c \\ y = - 4x - 42[/tex]
