Help me!!!!!!10 points best answer!!!!?

Question

Write the equation of a line perpendicular to the line 6x – 3y=10 and containing the point (-6, 2).

Answer 1

Seems as if I've answered this one already...

(1) Get the given line in Slope-Intercept form... y=mx+b
6x – 3y=1\

Add -6x to both sides...
-3y = 10-6x

Multiply both sides by -1/3
y = 2x - 10/3

The slope of the given line (m) is 2

The slope of a perpendicular to that line is the negative reciprocal of the slope of that line.... The reciprocal of 2 is 1/2, the negative reciprocal is -1/2. When you multiply a number by its reciprocal, you get 1. So, 2/7 and 7/2 are reciprocals. So are 3 and 1/3, (x+3)/(3x-2) and (3x-2)/(x+3)... see how it works?

So the perpendicular line is y= (-1/2)x + b... but we don't know what b is yet...
But we have a point on the line, (-6,2) So we know that whatever b is, 2=(-1/2)(-6) + b
So solve for b...2=3+b
Add -3 to both sides
b= -1
So the formula for the perpendicular is y=(-1/2)x - 1, or, if you prefer... y = -x/2 - 1

Answer 2

First, let's rewrite the equation of the line in y=mx+b form.

6x - 3y = 10
3y = 6x - 10
y = 2x - (10/3)

The slope of the original line is thus 2.
Therefore, the slope of a perpendicular line is (-1/2).

Hence, the perpendicular line we're looking for is:
y = (-1/2)x + b
Further, this line passes through the point (-6,2). This lets us solve for b, by plugging in -6 for x and 2 for y.

2 = (-1/2)*(-6) + b
2 = 3 + b
b = -1

The equation you're looking for is y = (-1/2)x - 1.

Hope that helps!

Answer 3

6x - 3y = 10
3y = 6x - 10
y = 2x - 10/3

Slope of the line is 2

The product of the slopes of perpendicular lines is -1.
The slope of the line perpendicular to this would be -1/2

y = -x/2 + c
When x=-6, y=2
2 = 3 + c
c = -1
y = -x/2 - 1

x + 2y + 2 = 0