Question

An equation is shown.
9x - 6y = 30
Which equation is an equivalent equation rewritten in slope-intercept form?

Answer 1

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:

\[ 9x - 6y = 30 \]

1. First, isolate the term with \( y \) on one side of the equation. Subtract \( 9x \) from both sides:

\[ -6y = -9x + 30 \]

2. Now, divide each term by \(-6\) to solve for \( y \):

\[ y = \frac{-9}{-6}x + \frac{30}{-6} \]

3. Simplifying both fractions:

\[ y = \frac{9}{6}x - 5 \]

4. Reducing \( \frac{9}{6} \) gives:

\[ y = \frac{3}{2}x - 5 \]

Therefore, the equivalent equation in slope-intercept form is:

\[ y = \frac{3}{2}x - 5 \]