Still need help on this one

Drawing a blank on this one, not sure where to start.

Find the equation, in standard form, with all integer coefficients, of the line perpendicular to x + 3y = 12 and passing through (9, -5).

Very easy

Recall that the slopes of perpendicular lines have slopes that are negative reciprocals of each other, or in other words, the product of their slopes is -1

Your first line is x + 3y = 12

So the perpendicular line must be

3x - y = c , the only thing we don't know is the constant
But (9,-5) lies on this new line
so 3(9) - (-5) = c
c = 32

The equation must be 3x - y = 32

I got something totally different -

x +3y = 12
x - x + 3y = 12 - x
3y = -x + 12
3y/3 = -x/3 + 12/3
y = -3x + 4
y - -5 = 1/3(x - 9)
y + 5 = 1/3x - 3
y + 5 - 5 = 1/3x - 3 - 5
y = 1/3x - 8

no!

the slope of the given line was -1/3, the slope of your new line is +1/3
So they are not even perpendicular!!

from your line:
3y/3 = -x/3 + 12/3 so far so good
now
y = (-1/3)x + 4
so the new slope must be +3

y + 5 = 3(x - 9)
y + 5 = 3x - 27
y = 3x - 32, which when rearranged is the same as 3x - y = 32

let me show you another approach

the slope of the given line was -1/3,

(continued)

so the slope of the new line must be +3

then the new equation is y = 3x + b
but (9,-5) lies on it
so -5 = (3)(9) + b
b = -32

for y = 3x - 32

Thank you so much.

To find the equation of a line perpendicular to a given line, you need to determine two things: the slope of the given line and the negative reciprocal of that slope.

First, let's rearrange the given equation, x + 3y = 12, into slope-intercept form (y = mx + b), where "m" is the slope and "b" is the y-intercept.

Start by subtracting "x" from both sides of the equation:
3y = -x + 12

Next, divide both sides by 3 to isolate "y":
y = (-1/3)x + 4

So, the slope of the given line is -1/3.

Since we want to find the line perpendicular to this one, we need to determine the negative reciprocal of the slope. The negative reciprocal is obtained by flipping the fraction and changing the sign.

The negative reciprocal of -1/3 is 3/1, which simplifies to 3.

Now that we have the slope of the perpendicular line, we can use the point-slope form of a linear equation to find the equation of the line passing through the point (9, -5).

The point-slope form of a linear equation is: y - y1 = m(x - x1), where (x1, y1) is a point on the line and "m" is the slope.

Substituting the values, we have:
y - (-5) = 3(x - 9)

Simplifying:
y + 5 = 3x - 27

To convert this equation into standard form, where all coefficients are integers, rearrange the equation by moving all terms to one side:
3x - y = 32

Therefore, the equation of the line perpendicular to x + 3y = 12 and passing through the point (9, -5) in standard form is 3x - y = 32.