I need to find the equation of the line

Mathematics

2 answers:

jolli1 [7]1 year ago

7 0

Answer:

y = 3x + 3

Step-by-step explanation:

See attached image.

deff fn [24]1 year ago

3 0

Answer:

y = 3x + 3

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 )

calculate m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line

m = $\frac{3-0}{0-(-1)}$ = $\frac{3}{0+1}$ = $\frac{3}{1}$ = 3

the line crosses the y- axis at (0, 3 ) ⇒ c = 3

y = 3x + 3 ← equation of line

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Show all work to identify the asymptotes and end behavior of the function f(x)= 5x/x-25.

jeyben [28]

Considering the given function and the asymptote concept, we have that:

The vertical asymptote is of x = 25.

The horizontal asymptote is of y = 5.

The end behavior is that as $x \rightarrow \infty, f(x) \rightarrow 5$ .

<h3>What are the asymptotes of a function f(x)?</h3>

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity. Hence it also gives the end behavior of the function.

In this problem, the function is:

$f(x) = \frac{5x}{x - 25}$ .

The vertical asymptote is found as follows:

x - 25 = 0 -> x = 25.

The horizontal asymptote is found as follows:

$y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{5x}{x - 25} = \lim_{x \rightarrow \infty} \frac{5x}{x} = \lim_{x \rightarrow \infty} 5 = 5$ .