The equation in the image is $3x + 4y = 12$. To graph this, let's find the intercepts and use them to plot the line.

Finding the intercepts:

1. For the x-intercept: Set $y = 0$ in the equation $3x + 4y = 12$. $3x + 4(0) = 12 \implies 3x = 12 \implies x = 4$ So, the x-intercept is $(4, 0)$.

2. For the y-intercept: Set $x = 0$ in the equation $3x + 4y = 12$. $3(0) + 4y = 12 \implies 4y = 12 \implies y = 3$ So, the y-intercept is $(0, 3)$.

Plotting:

• The x-intercept is $(4, 0)$.
• The y-intercept is $(0, 3)$.

To graph the line, plot these two points $(4, 0)$ and $(0, 3)$ on the grid and connect them with a straight line.

Let me know if you'd like to see further details, or if you have any other questions! Here are some related questions:

1. How do you find the slope of the line from the equation?
2. How can you rewrite the equation $3x + 4y = 12$ in slope-intercept form?
3. What is the slope of this line, and how does it relate to the intercepts?
4. How would the graph change if the equation were $3x + 4y = 8$?
5. What are the general steps to graph any linear equation?

Tip: When graphing lines, finding both intercepts can quickly provide two key points to sketch the line.