What is the slope of the line that passes through the points left bracket, minus, 4, comma, 6, right bracket(−4,6) and left bracket, minus, 4, comma, 18, right bracket(−4,18)? Write your answer in simplest form.
The slope of a line passing through two points, (x₁,y₁) and (x₂,y₂), can be found using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
In this case, the points are (-4,6) and (-4,18), so the x-coordinates are the same (-4). The y-coordinates are 6 and 18, respectively.
Substituting these values into the formula:
m = (18 - 6) / (-4 - (-4))
m = 12 / 0
m = undefined
The slope of the line passing through these two points is undefined, as there is no change in the x-coordinate.