Problem

Consider the equation $1.5 x+4.5 y=18$.
1 If we graph the equation, what is the slope of the graph?
Where does the graph intersect the $y$-axis? Write as a coordir
Where does it intersect the $\mathrm{x}$-axis? Write as a coordinate

Answer

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Answer

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 \(\boxed{(12, 0)}\).

Steps

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 \(\boxed{(12, 0)}\).

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