Answer:
Part A) The slope is undefined
Part B) The equation of the line is [tex]x=p[/tex]
Part C) None y-intercept
Part D) The slope of a line perpendicular to the given line is equal to zero
Step-by-step explanation:
we have that
Describe
A) slope of the line
B) equation of the line
C) y-intercept
D) slope of a line perpendicular to the given line
Part A) slope of the line
we know that
The 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 undefined
Its a vertical line (parallel to the y-axis)
Part B) Equation of the line
we know that
The 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-intercept
The y-intercept is the value of y when the value of x is equal to zero
The vertical line not intercept the y-axis
so
None y-intercept
Part D) slope of a line perpendicular to the given line
A line perpendicular to the given line is a horizontal line (parallel to the x-axis)
therefore
The slope is equal to zero
