SOLUTION: Find the general form of the equation of the line that passes through (-2,-5) and is perpendicular to the graph of 3x+2y=0 Can you please show me how to figure this out? I don't

Question 207553This question is from textbook
: Find the general form of the equation of the line that passes through (-2,-5) and is perpendicular to the graph of 3x+2y=0
Can you please show me how to figure this out? I don't even know where to begin. Thank you so very much for your help and for your time.
This question is from textbook

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given equation.

Subtract from both sides.

Divide both sides by to isolate y.

Simplify

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

Rewrite as

Distribute

Multiply

Subtract 5 from both sides.

Combine like terms. note: If you need help with fractions, check out this solver.

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

is .

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

.

RELATED QUESTIONS
Find the general form of the line perpendicular to 3x + 5y - 8 =0 that passes through the (answered by scott8148)

write the equation of the line in general form through (-5,-3) and is perpendicular to... (answered by Fombitz)

Line \ell_1 represents the graph of 3x + 2y = -14. Line \ell_2 passes through the point... (answered by ikleyn)

The equation, in general form, of the line that passes through the point (7,-7) and is... (answered by stanbon)

write the equation of the line that passes through (2 5) and perpendicular to the line... (answered by JulietG,mananth)

write the standard form of the equation of the line that passes through (5,-2) and is... (answered by scott8148)

Write the general form equation, Ax+By+C=0, of a line that passes through (7, 5) and is (answered by ikleyn)

What is the equation of the line written in standard form that passes through the point (answered by Fombitz)