1. ## slope and intercept

What is the slope and intercept of the following linear equation:
5(x+3y) - 3x + 2(5-y) = 15

2. Ok, so we have:

$5(x+3y) - 3x + 2(5-y) = 15$

We must completely expand it and resimplify:

First, we distribute:

$5x + 15y - 3x + 10 - 2y = 15$

Then we combine like terms:

$2x + 13y + 10 = 15$

Then we move the constant over:

$2x + 13y = 5$

Now, we isolate y:

$13y = 5 - 2x$

$y = \frac{5}{13} - \frac{2}{13}x$

This is in slope-intercept form, so we can derive the following from it:

$\text{y-intercept} = (0, \frac{5}{13})$

$\text{slope} = -\frac{2}{13}$

There you go.

3. Slope is $\frac{-2}{13}$