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How Do You Write an Equation for a Horizontal Line?

Write the equation of a horizontal line through (2,-1)

Summary

  1. "y=b" is the equation for a horizontal line
  2. We found out what "b" is just by plugging the y-coordinate of our point into the horizontal line equation!
  3. -1 is the y-coordinate that we are plugging into the equation y=b

Notes

    1. If the equation of a horizontal line DID depend on the x-value in any way, then the y-value would change depending on the x-value
    2. That means that there would be a non-horizontal slope, or steepness to the line.
    3. Remember, the slope of a horizontal line is 0
    1. Remember, the equation of our horizontal line is of the form "y=b"
    1. Our problem says that our line passes through the point (2,-1), so the point is on our line
    1. The point (2,-1) is on our line, so we might as well plug it in!
    1. We're plugging (2,-1) into the equation y=b
    1. We're plugging (2,-1) into the equation y=b
    1. We plugged (2,-1) into the equation y=b and got -1=b
    2. Since there was no "x" in the equation, we couldn't plug in the 2 of the point (2,-1)
    1. We solve our equation for "b" by plugging in the point (2,-1)!
    1. This is a shortcut for finding the equation of a horizontal line!
    2. Just set y equal to the y-coordinate of any point on the line
    1. We can just plug -1 in for "b" in the horizontal line equation!
    1. y=-1 is the equation of our horizontal line passing through the point (2,-1)
    1. We found this equation by plugging in the point (2,-1) into the horizontal line equation
    1. The equation for any horizontal line can be found just by looking at the y-coordinate of the points on that line
    1. The equation for any horizontal line can be found just by looking at the y-coordinate of the points on that line
    1. Just take the y-coordinate of any point on the horizontal line, and plug it into "b" of the horizontal line equation
    2. The horizontal line equation is "y=b"