Write the equation in slope-intercept form.

6x−3y=−18

To write the equation in slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we start by isolating \( y \) in terms of \( x \).

Given equation:
\[
6x - 3y = -18
\]

### Step 1: Move \( 6x \) to the other side of the equation
\[
-3y = -6x - 18
\]

### Step 2: Divide every term by \(-3\) to solve for \( y \)
\[
y = 2x + 6
\]

### Final Answer
The equation in slope-intercept form is:
\[
y = 2x + 6
\]

In this form:
- The slope \( m = 2 \)
- The y-intercept \( b = 6 \)

Would you like further details or have any questions?

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1. How do we find the slope and intercept from the standard form of an equation?
2. What is the slope-intercept form and its purpose?
3. How does changing the slope affect the line's steepness?
4. What happens if the y-intercept is negative?
5. Can you find the x-intercept of this equation?

**Tip:** To convert any linear equation to slope-intercept form, isolate \( y \) on one side by rearranging terms and dividing as needed.

Learn how to rewrite the linear equation 6x - 3y = -18 in slope-intercept form. This step-by-step solution helps students identify the slope and y-intercept of the line, suitable for Grades 7-9.

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