Let's solve the problem from the image. The equation given is:

$2y + 6x = 6$

Step 1: Simplify the equation

Solve for $y$ in terms of $x$ to rewrite the equation in slope-intercept form ($y = mx + b$):

$2y = -6x + 6$

$y = -3x + 3$

Step 2: Find two points

To graph the line, select at least two values for $x$, substitute them into the equation, and calculate the corresponding $y$-values.

Example:

1. Let $x = 0$: $y = -3(0) + 3 = 3$ Point: $(0, 3)$

2. Let $x = 2$: $y = -3(2) + 3 = -6 + 3 = -3$ Point: $(2, -3)$

Step 3: Plot these points

• Plot $(0, 3)$ on the graph.
• Plot $(2, -3)$ on the graph.

Step 4: Draw the line

Connect the two points with a straight line, and extend it across the graph.

Would you like a graphical solution or further clarification? Here are some related questions for practice:

1. What is the slope of the line $y = -3x + 3$, and how does it affect the graph?
2. How would the line change if the equation was $2y + 6x = 12$?
3. How can you determine the $y$-intercept and $x$-intercept from the equation?
4. How do you verify if a point (e.g., $(-1, 6)$) lies on the line $y = -3x + 3$?
5. What is the significance of graphing two points accurately?

Tip: Always choose simple $x$-values (like 0, 1, or 2) for substitution when finding points to plot a straight line.