To rewrite the equation \(5x - 19y = 7\) in slope-intercept form, which is \(y = mx + b\), we need to solve for \(y\).
Starting with the original equation:
\[ 5x - 19y = 7 \]
Subtract \(5x\) from both sides:
\[ -19y = -5x + 7 \]
Next, divide every term by \(-19\) to isolate \(y\):
\[ y = \frac{5}{19}x - \frac{7}{19} \]
Now the equation is in slope-intercept form, where \(m = \frac{5}{19}\) and \(b = -\frac{7}{19}\).
Thus, the final result is:
\[ y = \frac{5}{19}x - \frac{7}{19} \]