To solve the equation $2x - 6y = -6$ using intercepts and graph it on the grid:

Step 1: Find the x-intercept

To find the x-intercept, set $y = 0$ in the equation: $2x - 6(0) = -6 \implies 2x = -6 \implies x = -3$ So, the x-intercept is $(-3, 0)$.

Step 2: Find the y-intercept

To find the y-intercept, set $x = 0$ in the equation: $2(0) - 6y = -6 \implies -6y = -6 \implies y = 1$ So, the y-intercept is $(0, 1)$.

Step 3: Plot the intercepts

On the grid:

• Plot the point $(-3, 0)$ (x-intercept).
• Plot the point $(0, 1)$ (y-intercept).

Step 4: Draw the line

Connect the two points with a straight line to graph the equation.

Let me know if you'd like me to provide additional calculations or further clarify this process!

Follow-Up Questions:

1. What happens if the coefficients of $x$ or $y$ change in a linear equation?
2. How can you verify that your graphed line is correct using substitution?
3. What is the slope of the line $2x - 6y = -6$, and how can it be calculated from the equation?
4. How would you graph the equation if you were given it in slope-intercept form ($y = mx + b$)?
5. What does it mean if two lines have the same slope but different y-intercepts?

Tip:

To double-check your graph, you can test any additional point (besides the intercepts) by substituting its coordinates into the original equation. If the equation holds true, the point lies on the line!