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Juliette [100K]
3 years ago
6

What is the equation of the line that is parallel to y = 1/5 x + 4 and that passes through (5,–4)?

Mathematics
1 answer:
nignag [31]3 years ago
8 0

Answer:

y = \frac{1}{5} x - 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = \frac{1}{5} x + 4 ← is in slope- intercept form

with slope m = \frac{1}{5}

Parallel lines have equal slopes, thus

y = \frac{1}{5} x + c ← is the partial equation

To find c substitute (5, - 4) into the partial equation

- 4 = 1 + c ⇒ c = - 4 - 1 = - 5

y = \frac{1}{5} x - 5 ← equation of parallel line

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According to the theory of <em>rational</em> functions, there are no <em>vertical</em> asymptotes at the <em>rational</em> function evaluated at x = 3.

<h3>What is the behavior of a functions close to one its vertical asymptotes?</h3>

Herein we know that the <em>rational</em> function is q(x) = (x² - 6 · x + 9) / (x² - 8 · x + 15), there are <em>vertical</em> asymptotes for values of x such that the denominator becomes zero. First, we factor both numerator and denominator of the equation to see <em>evitable</em> and <em>non-evitable</em> discontinuities:

q(x) = (x² - 6 · x + 9) / (x² - 8 · x + 15)

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There are one <em>evitable</em> discontinuity and one <em>non-evitable</em> discontinuity. According to the theory of <em>rational</em> functions, there are no <em>vertical</em> asymptotes at the <em>rational</em> function evaluated at x = 3.

To learn more on rational functions: brainly.com/question/27914791

#SPJ1

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