Question

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 1

Part A) The slope is undefined

Part B) The equation of the line is
`x=p`

Part C) None y-intercept

Part D) The slope of a line perpendicular to the given line is equal to zero

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

`m=(y2-y1)/(x2-x1)`

we have

`(p,a)\ (p,-a)`

Substitute the values

`m=(-a-a)/(p-p)`

`m=(-2a)/(0)` -----> 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

`x=p`

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