What is the slope and intercept of the following linear equation:
5(x+3y) - 3x + 2(5-y) = 15
Ok, so we have:
$\displaystyle 5(x+3y) - 3x + 2(5-y) = 15$
We must completely expand it and resimplify:
First, we distribute:
$\displaystyle 5x + 15y - 3x + 10 - 2y = 15$
Then we combine like terms:
$\displaystyle 2x + 13y + 10 = 15$
Then we move the constant over:
$\displaystyle 2x + 13y = 5$
Now, we isolate y:
$\displaystyle 13y = 5 - 2x$
$\displaystyle y = \frac{5}{13} - \frac{2}{13}x$
This is in slope-intercept form, so we can derive the following from it:
$\displaystyle \text{y-intercept} = (0, \frac{5}{13})$
$\displaystyle \text{slope} = -\frac{2}{13}$
There you go.