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.