Write the equation of the line that passes through the points left bracket, 6, comma, minus, 9, right bracket(6,−9) and left bracket, 6, comma, 9, right bracket(6,9). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
To find the equation of the line passing through the points (6, -9) and (6, 9), we must first determine the slope of the line.
The slope (m) of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the coordinates of the given points, we have:
m = (9 - (-9)) / (6 - 6)
m = 18 / 0
Since the denominator is zero, we can conclude that the line is vertical. A vertical line has an undefined slope.
Therefore, the equation of the line passing through the points (6, -9) and (6, 9) is x = 6.