Put the following equation of a line into slope-intercept form, simplifying all fractions.

3, x, minus, 6, y, equals, minus, 30

3*x*−6*y*=

−30

To convert the equation \( 3x - 6y = -30 \) into slope-intercept form (\( y = mx + b \)), we need to solve for \( y \).

### Step 1: Move the \( 3x \) term to the other side.
\[
-6y = -3x - 30
\]

### Step 2: Divide the entire equation by \(-6\) to isolate \( y \).
\[
y = \frac{-3x}{-6} + \frac{-30}{-6}
\]

### Step 3: Simplify the fractions.
\[
y = \frac{1}{2}x + 5
\]

So, the slope-intercept form of the line is:
\[
y = \frac{1}{2}x + 5
\]

Would you like any details or further clarification on this process? 

Here are 5 related questions:
1. What is the slope of the line in the equation \( y = \frac{1}{2}x + 5 \)?
2. How would you graph the line \( y = \frac{1}{2}x + 5 \)?
3. Can you rewrite \( y = \frac{1}{2}x + 5 \) in standard form?
4. What does the y-intercept represent in the equation \( y = \frac{1}{2}x + 5 \)?
5. How would the slope-intercept equation change if the slope were doubled?

**Tip:** The slope \( m \) in the slope-intercept form \( y = mx + b \) tells you how steep the line is, while \( b \) gives the y-intercept, where the line crosses the y-axis.

Put the following equation of a line into slope-intercept form, simplifying all fractions: 3x - 6y = -30.

Learn how to convert the equation 3x - 6y = -30 into slope-intercept form (y = mx + b) with a step-by-step guide. This solution simplifies all fractions and helps you understand key algebraic concepts. Suitable for students in Grades 7-9.

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