The slope of the line passing through the points A(a, b), and B(c, d), is given by
[tex]\displaystyle{ m=\frac{d-b}{c-a}, [/tex]
thus, the slope of the line through points (p, a) and (p, –a) is
[tex]\displaystyle{ m=\frac{-a-a}{p-p}=\frac{-2a}{0}. [/tex]
When applying the slope formula results in division by zero, this means that the line is a vertical line.
This could have also been noticed directly, since the line contains 2 points with the same x-coordinate.
The equation of this line is x=p, since the x-coordinate is always p, no matter what y is.
If p=0, then the equation of the line is x=0, which is the y-axis itself. In this case, the y-intercept is the whole y-axis.
Answer: The whole y-axis.
