SOLUTION: Find the equation, in standard form, of the line perpendicular to 2x - 3y = -5 and passing through (3,-2). Write the equation in standard form, with all integer coefficients.

Question 183043: Find the equation, in standard form, of the line perpendicular to 2x - 3y = -5 and passing through (3,-2). Write the equation in standard form, with all integer coefficients.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given equation.

Subtract from both sides.

Rearrange the terms.

Divide both sides by to isolate y.

Break up the fraction.

Reduce.

We can see that the equation has a slope and a y-intercept .

Now to find the slope of the perpendicular line, simply flip the slope to get . Now change the sign to get . So the perpendicular slope is .

Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope and the coordinates of the given point

.

Start with the point slope formula

Plug in , , and

Rewrite as

Multiply both sides by 2.

Distribute

Add 3x to both sides.

Subtract 4 from both sides.

Combine like terms.

===============================================

Answer:

So the equation of the line perpendicular to that goes through the point

in standard form is .

So the answer you're looking for is:

Here's a graph to visually verify our answer:
Graph of the original equation (red) and the perpendicular line (green) through the point

.

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