# What is the slope of 8y=21y-44x+21?

Mar 14, 2018

The slope should be 44/13

#### Explanation:

We need to get the problem equation into the slope-intercept form $y = m x + b$. In order to do that, we'll need to get all y-terms to the left-hand side of the equation (LHS), and then divide through by y's coefficient:

$8 y = 21 y - 44 x + 21$

First, let's subtract $21 y$ from both sides, effectively moving the 21y to the LHS:

$8 y - 21 y = \cancel{21 y} - 44 x + 21 - \cancel{21 y} \Rightarrow - 13 y = - 44 x + 21$

Now, we'll divide through by y's coefficient, -13:

$\frac{- 13}{- 13} y = \left(\frac{- 44}{-} 13\right) x + \frac{21}{-} 13$

$y = \frac{44}{13} x - \frac{21}{13}$

We cannot reduce further since 13 is prime. Our slope is x's coefficient, which is $\frac{44}{13}$.