What is the equation of the line that passes through points -2 -3 and is perpendicular to 2x minus 3y equals 6?

Answer 1

We know that if it is perpendicular to the line 2x-3y-6=0 or better yet, the line y=(2/3)x-2 (I just rearranged the equation from its standard form), the m-value (slope) of the new line must become inverted (3/2) and negative (-3/2). When you invert the m-value and change it's sign, you are finding the perpendicular value to the original.

So for our new equation we have y=(-3/2)x-2

We're not done yet! This new line does not go through the specified point (-2,-3).

To find the vertical shift (which will allow the line to pass through (-2,-3)) we will sub this point (-2,-3) into the new equation we found, but we will omit the shift value and replace it with a variable "b".

Now we have:

(-3)=(-3/2)(-2)+b

(-3)=(3)+b

b=(-6)

Finally, we can put together our equation.

y=(-3/2)x-6 - or in standard form: 3x+2y+6=0