Description
What is the slope of a line parallel to the line x = 5? Please explain how you arrived at your answer.
Explanation & Answer
Attached.
What is the slope of a line parallel to x=5.
Def. of Parallel: Two lines that never intersect. They do not intersect because they have the
𝑦 −𝑦
same “slope”. “Slope” is the rate of change of a linear function given by m= 𝑥2 𝑥 1 where (x1,y1)
2− 1
and (x2,y2) are arbitrary, but different points that lie on the line. “Slope” is interchangeable with
“rate of change”. 2 parallel lines can be thought of as the same line + (plus or minus) and
arbitrary vertical phase shift (a.k.a. they have different y-intecepts and the difference between
the “b” values is the phase shift).
Background: To be “on the line means” that a point (x0,y0) satisfies: Ax+By=C (standard form of
a line) where A,B,C are arbitrary constants and if B=0 the equation cannot be written in the
well-known “slope-intercept form”~y=mx+b. This statement is back by the fact that if B=0
division is impossible in attempting to manipulate the standard form of the equation in order to
solve for y.
Answer: With the aforementioned in mind, x=5 describes a vertical line, all points (5, y), which
𝑦 −𝑦1
m= 𝑥2
2− 𝑥1
leads the denominator as zero (since x2 always equals x1), therefore m is undefined.
Therefore the answer to your question is undefined. X=1, x=2, x=-100, x=k are all parallel and all
have an “undefined slope”.
The slope is considered undefined because division by zero is impossible (undefined).
(Note: Some people may say that dividing by zero is infinity and although limits as x approach
zero tend to infinity that limit ...
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