What is the equation of the line that passes through (–2, –3) and is perpendicular to 2x – 3y = 6?

Step-by-step explanation:

Since the line needs to be perpendicular to , that means the slope of the line must be the opposite reciprocal. Rearrange the equation  to solve for the value of y, with variable y on the left side.

So, the slope of the line given already is . The opposite reciprocal of this is .

From what information we know so far (the slope) about the equation of the line we are trying to find, we can write a basic equation that allows us to solve for the y-intercept. Use the equation , where m is the slope (which we already found) and b is the y-intercept.

Since we are given a set of coordinate points that the line must pass through, we can substitute (-2, -3) in for x and y in the equation above. Then, solve for the value of b, which is our y-intercept.

Now we have all the necessary information to create our equation.