if the slope of a line is undefined, what is the point slope form?
coordinate C (-2,-2) d (1,-2)
If the slope of a line is undefined, it means that the line is vertical. In this case, we cannot write the equation of the line in the point-slope form, as this form requires a non-vertical line.
The point-slope form of the equation of a line is given by:
y - y₁ = m(x - x₁)
where (x₁, y₁) represents a point on the line, and m represents the slope of the line.
However, when the slope is undefined, we cannot determine a specific value for m.
In your case, the points given are C(-2, -2) and D(1, -2). Notice that the y-coordinates of both points are the same. This indicates that the line connecting these points is a horizontal line, not a vertical line.
For a horizontal line, the slope is always 0. Therefore, the equation of the line passing through C(-2, -2) and D(1, -2) can indeed be written in the point-slope form, using the slope of 0:
y - (-2) = 0(x - (-2))
Simplifying the equation, we get:
y + 2 = 0
Or, rearranging it, we have:
y = -2
So, the point-slope form of the equation for a horizontal line passing through points C(-2, -2) and D(1, -2) is y = -2.