Question: Sketch a graph of $$9x + 6y = 12$$
1. **State the problem:** We need to graph the linear equation $$9x + 6y = 12$$ using intercepts.
2. **Formula and rules:** To graph using intercepts, find where the line crosses the x-axis and y-axis.
- The x-intercept is found by setting $$y=0$$ and solving for $$x$$.
- The y-intercept is found by setting $$x=0$$ and solving for $$y$$.
3. **Find the x-intercept:**
Set $$y=0$$ in the equation:
$$9x + 6(0) = 12$$
$$9x = 12$$
Divide both sides by $$9$$:
$$\cancel{9}x = \frac{12}{\cancel{9}}$$
$$x = \frac{12}{9} = \frac{4}{3}$$
So, the x-intercept is $$\left(\frac{4}{3}, 0\right)$$.
4. **Find the y-intercept:**
Set $$x=0$$ in the equation:
$$9(0) + 6y = 12$$
$$6y = 12$$
Divide both sides by $$6$$:
$$\cancel{6}y = \frac{12}{\cancel{6}}$$
$$y = 2$$
So, the y-intercept is $$(0, 2)$$.
5. **Plot the points:**
Plot the points $$\left(\frac{4}{3}, 0\right)$$ and $$(0, 2)$$ on the coordinate grid.
6. **Draw the line:**
Draw a straight line through these two points. This line represents the graph of $$9x + 6y = 12$$.
**Final answer:** The graph is a straight line crossing the x-axis at $$\left(\frac{4}{3}, 0\right)$$ and the y-axis at $$(0, 2)$$.