Aline passes through the points (p, a) and (p, –a) where p and a are real numbers. if p=0, what is the y-intercept? explain your reasoning.

The slope of the line passing through the points A(a, b), and B(c, d), is given by 
                               

thus, the slope of the line through points (p, a) and (p, –a) is 

                               

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.

The whole y-axis.