Question

graph $-9x + 6y = 18$.

Explanation:

Step1: Rewrite in slope - intercept form

We start with the equation \(-9x + 6y=18\). We want to solve for \(y\) to get it in the form \(y = mx + b\) (where \(m\) is the slope and \(b\) is the \(y\) - intercept).
First, add \(9x\) to both sides of the equation: \(6y=9x + 18\).
Then, divide each term by \(6\): \(y=\frac{9}{6}x+\frac{18}{6}\), which simplifies to \(y=\frac{3}{2}x + 3\). Wait, but the graph shown is a horizontal line \(y = 5\). There must be a mistake in the initial analysis. Let's re - examine the equation. If the graph is \(y = 5\), then we can substitute \(y = 5\) into the original equation \(-9x+6y = 18\) and solve for \(x\) to find the \(x\) - coordinates of the points.
Substitute \(y = 5\) into \(-9x+6y=18\): \(-9x+6\times5 = 18\).

Step2: Solve for \(x\)

Simplify the left - hand side: \(-9x + 30=18\).
Subtract \(30\) from both sides: \(-9x=18 - 30=-12\).
Divide both sides by \(-9\): \(x=\frac{-12}{-9}=\frac{4}{3}\approx1.33\). But the points on the graph are at \(x=-5\) and \(x = 5\) with \(y = 5\). Let's check the original equation with \(y = 5\): \(-9x+6\times5=18\Rightarrow-9x=18 - 30=-12\Rightarrow x=\frac{4}{3}\). The graph in the picture seems incorrect for the equation \(-9x + 6y=18\). But if we assume that we want to graph \(y = 5\) (as per the given graph), we can find two points on the line \(y = 5\). For any \(x\) - value, \(y = 5\). So when \(x=-5\), \(y = 5\) (the point \((-5,5)\)) and when \(x = 5\), \(y = 5\) (the point \((5,5)\)). To graph the line \(-9x+6y = 18\) correctly:
Rewrite it in slope - intercept form: \(6y=9x + 18\Rightarrow y=\frac{3}{2}x+3\). The \(y\) - intercept is \(b = 3\) (the point \((0,3)\)) and the slope \(m=\frac{3}{2}\). To find another point, we can use the slope. From \((0,3)\), we move up \(3\) units and right \(2\) units to get the point \((2,6)\).

But since the given graph is a horizontal line \(y = 5\), let's work with the graph. The line \(y = 5\) is a horizontal line with slope \(m = 0\) and \(y\) - intercept \(b = 5\). To graph \(y = 5\), we plot two points with \(y\) - coordinate \(5\) (like \((-5,5)\) and \((5,5)\)) and draw a line through them.

If we want to graph the equation \(-9x + 6y=18\) correctly:

1. Find the \(y\) - intercept: Set \(x = 0\), then \(6y=18\Rightarrow y = 3\). So the point is \((0,3)\).
2. Find the \(x\) - intercept: Set \(y = 0\), then \(-9x=18\Rightarrow x=-2\). So the point is \((-2,0)\).
3. Plot the points \((0,3)\) and \((-2,0)\) and draw a line through them.

Answer:

To graph \(y = 5\) (as per the given graph), plot points \((-5,5)\) and \((5,5)\) (or any two points with \(y = 5\)) and draw a horizontal line. To graph \(-9x + 6y=18\) correctly, plot \((0,3)\) and \((-2,0)\) and draw a line through them.