To solve the given problem, we will:

1. Rewrite the equation in slope-intercept form ($y = mx + b$).
2. Identify the slope ($m$) and the $y$-intercept ($b$).
3. Provide the necessary information to graph the line.

Step 1: Rewrite in slope-intercept form

The equation is: $-12x + 3y = 3$

Add $12x$ to both sides: $3y = 12x + 3$

Divide through by 3: $y = 4x + 1$

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

From the equation $y = 4x + 1$:

• Slope ($m$): $4$
• $y$-intercept ($b$): $1$

Step 3: Instructions to graph

1. Start by plotting the $y$-intercept at $(0, 1)$ on the graph.
2. Use the slope $m = 4$, which means "rise over run" = $4/1$. From the point $(0, 1)$, move up 4 units and to the right 1 unit to plot another point $(1, 5)$.
3. Draw a straight line through the two points.

Would you like a visual demonstration or further explanation?

Here are 5 related questions for further exploration:

1. How do you interpret the slope and $y$-intercept in a real-world context?
2. Can you determine the $x$-intercept of this line?
3. What would happen to the graph if the slope were negative?
4. How would the graph shift if the $y$-intercept changed to $-2$?
5. Can you convert the equation $y = 4x + 1$ back to standard form?

Tip: Always check your slope direction when plotting the second point to ensure accuracy.