What is the slope of the line that passes through the points left bracket, 6, comma, 10, right bracket(6,10) and left bracket, 6, comma, minus, 2, right bracket(6,−2)? Write your answer in simplest form.
The slope of a line passing through two points (x₁,y₁) and (x₂,y₂) can be found by using the formula:
slope = (y₂ - y₁) / (x₂ - x₁)
Using the points (6,10) and (6,-2):
slope = (-2 - 10) / (6 - 6)
slope = (-12) / (0)
The denominator is zero, which means the line is vertical. A vertical line does not have a well-defined slope.