To graph the equation (x = 3y + 6), we can rearrange it into slope-intercept form ((y = mx + b)), where (m) is the slope and (b) is the y-intercept.
[ x = 3y + 6 ]
Subtract (6) from both sides:
[ x - 6 = 3y ]
Divide both sides by (3):
[ frac{x - 6}{3} = y ]
So, the equation in slope-intercept form is (y = frac{1}{3}x - 2).
Now, we can use this information to plot points and draw the graph. Here's a sample Cartesian plane:
The two points plotted are ((4, 0)) and ((0, -2)), and you can draw a line passing through these points to represent the graph of the equation (x = 3y + 6).
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