A line passes through the points (p, a) and (p, –a) where p and a are real numbers and p ≠ 0. Describe each of the following. Explain your reasoning.

Answer:Part A) The slope is undefinedPart B) The equation of the line is [tex]x=p[/tex]Part C) None y-interceptPart D) The slope of a line perpendicular to the given line is equal to zeroStep-by-step explanation:we have thatDescribeA) slope of the line B) equation of the line C) y-intercept D) slope of a line perpendicular to the given linePart A) slope of the line we know thatThe formula to calculate the slope between two points is equal to [tex]m=\frac{y2-y1}{x2-x1}[/tex] we have [tex](p,a)\ (p,-a)[/tex] Substitute the values [tex]m=\frac{-a-a}{p-p}[/tex] [tex]m=\frac{-2a}{0}[/tex]  -----> the slope is undefinedIts a vertical line (parallel to the y-axis)Part B) Equation of the linewe know thatThe equation of a vertical line is equal to the x-coordinate of the points through which the line passes.so[tex]x=p[/tex]Part C) The y-interceptThe y-intercept is the value of y when the value of x is equal to zeroThe vertical line not intercept the y-axissoNone y-interceptPart D) slope of a line perpendicular to the given lineA line perpendicular to the given line is a horizontal line (parallel to the x-axis)thereforeThe slope is equal to zero