To rewrite the equation \(9x + 15y - 8 = 0\) 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:
\[ 9x + 15y - 8 = 0 \]
First, isolate the \(y\) term. Add \(8\) to both sides:
\[ 9x + 15y = 8 \]
Next, subtract \(9x\) from both sides:
\[ 15y = -9x + 8 \]
Now, divide every term by \(15\) to solve for \(y\):
\[ y = -\frac{9}{15}x + \frac{8}{15} \]
Now simplify \(-\frac{9}{15}\):
\[ y = -\frac{3}{5}x + \frac{8}{15} \]
So, the equation in slope-intercept form is:
\[ y = -\frac{3}{5}x + \frac{8}{15} \]