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

To put the equation \(3x - 3y = 15\) into slope-intercept form, we need to solve for \(y\).

### Step 1: Subtract \(3x\) from both sides
\[
-3y = -3x + 15
\]

### Step 2: Divide both sides by \(-3\) to solve for \(y\)
\[
y = \frac{-3x + 15}{-3}
\]

### Step 3: Simplify the fractions
\[
y = \frac{-3x}{-3} + \frac{15}{-3}
\]
\[
y = x - 5
\]

Thus, the equation in slope-intercept form is:
\[
y = x - 5
\]

### Final form:
The slope-intercept form is \(y = x - 5\), where the slope \(m = 1\) and the y-intercept \(b = -5\).

Would you like further details or have any questions? Here are some related questions:

1. How do you determine the slope and y-intercept from a given equation?
2. What is the geometric interpretation of the slope?
3. How does changing the slope affect the graph of a line?
4. How can you find the x-intercept of a line given its equation?
5. How do you convert a slope-intercept form back into standard form?

**Tip**: In slope-intercept form \(y = mx + b\), the coefficient \(m\) represents the slope of the line and \(b\) is the y-intercept.

Learn how to convert the equation 3x - 3y = 15 into slope-intercept form (y = mx + b), simplifying all fractions. This algebraic problem covers key concepts such as linear equations and slope-intercept form, suitable for students in Grades 8-10.

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