Put the following equation of a line into slope-intercept form, simplifying all fractions.3, y, minus, 3, x, equals, 153y−3x=15

1. ### Break Down the Problem

We need to rearrange the equation $3y - 3x = 15$ into slope-intercept form, which is given by $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

2. ### Relevant Concepts

To convert the equation into slope-intercept form, we need to isolate $y$ on one side of the equation. This involves adding $3x$ to both sides and then dividing by $3$.

3. ### Analysis and Detail

1. Start with the equation: $3y - 3x = 15$
2. Add $3x$ to both sides: $3y = 3x + 15$
3. Divide all terms by $3$: $y = x + 5$

4. ### Verify and Summarize

We can verify this by rechecking the steps and confirming that the equation satisfies the original format. The slope is $1$ and the y-intercept is $5$.

Final Answer

The slope-intercept form of the equation is: $y = x + 5$