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Write the equation of the line that passes through the points 
(2,6) and 
(5,6). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
Answer:

Write the equation of the line that passes through the points (2,6) (2,6) and (5,6) (5,6) . Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.\newlineAnswer:

Full solution

Q. Write the equation of the line that passes through the points (2,6) (2,6) and (5,6) (5,6) . Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.\newlineAnswer:
  1. Determine Line Type: First, we need to determine if the line is vertical, horizontal, or neither. We can do this by looking at the xx and yy coordinates of the two points. If the xx-coordinates are the same, the line is vertical. If the yy-coordinates are the same, the line is horizontal. If neither are the same, the line is neither vertical nor horizontal.
  2. Identify Horizontal Line: We observe that the yy-coordinates of both points (2,6)(2,6) and (5,6)(5,6) are the same, which means the line is horizontal. For a horizontal line, the slope mm is 00, because there is no change in the yy-value as the xx-value changes.
  3. Calculate Slope: Since the line is horizontal, its equation is of the form y=ky = k, where kk is the constant yy-value for all points on the line. In this case, kk is equal to 66, because that is the yy-coordinate for both points given.
  4. Find Equation: Therefore, the equation of the line that passes through the points (2,6)(2,6) and (5,6)(5,6) is y=6y = 6.

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