To rewrite the equation \(6x - 8y = -19\) in slope-intercept form (which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept), we need to solve for \(y\).
Starting with the original equation:
\[ 6x - 8y = -19 \]
- Subtract \(6x\) from both sides:
\[ -8y = -6x - 19 \]
- Divide every term by \(-8\) to solve for \(y\):
\[ y = \frac{-6}{-8}x + \frac{-19}{-8} \]
- Simplify the fractions:
\[ y = \frac{3}{4}x + \frac{19}{8} \]
Thus, the equation in slope-intercept form is:
\[ y = \frac{3}{4}x + \frac{19}{8} \]