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Graph the equation 2 y=6 using the form y = mx + b. (1 point)

Graph one (0,-6) (1,-5)
Graph 2 (0,-4) (1,-10)
Graph 3 (0,0) (6,6)
Graph 4 (0,3) (3,2)

1 answer

To graph the equation \(2y = 6\), we first convert it into the form \(y = mx + b\):

  1. Start with the given equation:
    \(2y = 6\)

  2. Divide both sides by 2:
    \(y = 3\)

This tells us that the equation represents a horizontal line where \(y\) is always 3, regardless of the value of \(x\).

Now let's analyze the answer choices based on the information about the horizontal line at \(y = 3\).

  • Graph 1 (0,-6) (1,-5): This graph is decreasing; does not represent \(y = 3\).
  • Graph 2 (0,-4) (1,-10): This graph is also decreasing; does not represent \(y = 3\).
  • Graph 3 (0,0) (6,6): This graph is increasing; does not represent \(y = 3\).
  • Graph 4 (0,3) (3,2): The point (0, 3) is valid for \(y = 3\), but the point (3, 2) is below \(y = 3\); thus it does not represent the entire line.

Since none of the provided graphs accurately represent the equation \(y = 3\) (a horizontal line at \(y = 3\)), we can conclude that none of the choices given match the equation \(2y = 6\).