Question

Can someone please explain how this slope equation was obtained for this double integral?

Answer 1

I don't understand where $$ x + 3y = 7 $$ comes from (which is used to get the upper bound of the inside integral)

Answer 2

I know for the slope equation, I have: $$ y - y_0 = m(x-x_0) $$
which comes out to
$$ (-1) = m(3)\ \ => \ \ m = -\frac{1}{3} $$

Answer 3

that is about all i can understand
it is the equation of the line

Answer 4

So I guess I could plug that into $$ y = mx + b $$
$$ y = -\frac{x}{3} + b $$
$$ b = \frac{x}{3} + y $$

Answer 5

$$ y = mx + b $$
$$ y - b = mx $$
$$ y - b = -\frac{1}{3} x$$
$$ 3y - 3b = -x $$
$$ -3y +3b = -x $$
$$ 3b = -x + 3y $$
$$ b = -\frac{x}{3} + y $$

Answer 6

Seems to be no matter what way I do it, I can't get the slope equation to equal $$ x+3y = b $$

Answer 7

How did you arrive at \[-\frac{ 1 }{ 3 }\]

Answer 8

$$ (y- y_0) = m(x-x_0) $$
$$ (1 - 2) = m (4 - 1)$$
$$ (-1) = m(3) $$
$$ m = -\frac{1}{3} $$

Answer 9

\[y-2=-\frac{1}{3}(x-1)\]
\[-3y+6=x-1\]
\[x+3y=7\]

Answer 10

THANK. YOU.

Answer 11

It's the simple parts of math that always get me :)

Answer 12

yw
loathe calc 3, like finding equations of lines

Answer 13

lol, it is always that damned algebra!!

Answer 14

Ha ha