Answer:
y = -2 /3 x - 6
Step-by-step explanation:
Here we remind ourselves that if we have an equation of the form

then the equation of a line perpendicular to the above line is

where c is the y-intercept.
Now for our case, the equation we have is

which isn't helpful since we cannot use it to find the equation of the perpendicular line.
Therefore, to make it useful, we first convert it to the slope-intercept form: y = mx + b.
Now, subtracting 3x from both sides gives


dividing both sides by -2 gives


Now that our equation is in slope-intercept form, we can find the equation for the perpendicular line.
The equation of the line that is prependicular to the above line is


Now, we are told that this line must pass through (0, -6). Therefore, we have to find a value of b such that the above line passes through (0, -6). To find b, we put x = 0 and y = -6 into the above equation to get


The value of b is -6.
Therefore, the equation of a line perpendicular to 3x - 2y = 5 line passing through (0, -6) is
