Step 1 :Consider the equation \(1.5x + 4.5y = 18\).
Step 2 :We need to find the slope of the graph, the y-intercept, and the x-intercept.
Step 3 :The slope of the graph of a linear equation in the form \(y = mx + b\) is given by the coefficient of \(x\), which is \(m\). In this case, the equation is not in this form, so we need to rearrange it to find the slope.
Step 4 :Rearranging the equation, we get \(y = 4 - 0.333333333333333x\). So, the slope of the graph is \(-0.333333333333333\).
Step 5 :The y-intercept of the graph is the value of \(y\) when \(x = 0\). We can find this by setting \(x = 0\) in the equation and solving for \(y\). Doing this, we get \(y = 4\). So, the graph intersects the y-axis at \((0, 4)\).
Step 6 :The x-intercept of the graph is the value of \(x\) when \(y = 0\). We can find this by setting \(y = 0\) in the equation and solving for \(x\). Doing this, we get \(x = 12\). So, the graph intersects the x-axis at \((12, 0)\).
Step 7 :Final Answer: The slope of the graph of the equation is \(\boxed{-0.333333333333333}\). The graph intersects the y-axis at \(\boxed{(0, 4)}\) and the x-axis at \(\boxed{(12, 0)}\).