Consider the following equation.

6x−3y=36x−3y=3

Step 1 of 3 :  

Find the slope and y-intercept. Simplify your answer.

We are given the equation:

\[
6x - 3y = 3
\]

To find the slope and y-intercept, we need to rewrite the equation in the **slope-intercept form** \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

### Step 1: Solve for \( y \)

Start by isolating \( y \) in the given equation:
\[
6x - 3y = 3
\]
Subtract \( 6x \) from both sides:
\[
-3y = -6x + 3
\]
Now, divide through by \( -3 \) to get \( y \) by itself:
\[
y = 2x - 1
\]

### Step 2: Identify the slope and y-intercept

From the equation \( y = 2x - 1 \), we can now identify:
- The **slope** \( m = 2 \)
- The **y-intercept** \( b = -1 \)

### Final Answer:
- **Slope**: \( 2 \)
- **Y-intercept**: \( -1 \)

Would you like a more detailed explanation of the process?

Here are some additional questions related to this topic:
1. How do you determine the slope from an equation in general form?
2. What is the importance of slope and y-intercept in graphing linear equations?
3. How would the graph look if the slope were negative?
4. Can two different equations have the same slope?
5. What changes when the y-intercept is zero?

**Tip:** The slope tells you how steep a line is, while the y-intercept tells you where the line crosses the y-axis.

Consider the following equation. 6x - 3y = 3. Find the slope and y-intercept. Simplify your answer.

Learn how to find the slope and y-intercept of the linear equation 6x - 3y = 3. This step-by-step guide demonstrates the use of the slope-intercept form and simplifies the solution. Ideal for students in Grades 8-10 learning algebraic concepts.

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