To rewrite the equation \( 9x - 6y = 30 \) in slope-intercept form, we want to solve for \( y \) in terms of \( x \). The slope-intercept form is given by the equation \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
Starting with the original equation:
\[ 9x - 6y = 30 \]
- First, isolate the term with \( y \) on one side of the equation. Subtract \( 9x \) from both sides:
\[ -6y = -9x + 30 \]
- Now, divide each term by \(-6\) to solve for \( y \):
\[ y = \frac{-9}{-6}x + \frac{30}{-6} \]
- Simplifying both fractions:
\[ y = \frac{9}{6}x - 5 \]
- Reducing \( \frac{9}{6} \) gives:
\[ y = \frac{3}{2}x - 5 \]
Therefore, the equivalent equation in slope-intercept form is:
\[ y = \frac{3}{2}x - 5 \]