Find the horizontal asymptote, if any, of the graph of the rational function
\[
f(x)=\frac{-3 x+5}{5 x-4}
\]
(A) no horizontal asymptote
\[
y=-
\]
B
\[
y=-
\]
(C)
\[
\frac{5}{4}
\]
(D) $y=-3$

Answer

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Answer

$\boxed{y = -\frac{3}{5}}$ or $\boxed{y = -0.6}$ is the horizontal asymptote of the given rational function.

Steps

Step 1 ：Compare the degrees of the numerator and denominator. In this case, both degrees are equal (both are 1).

Step 2 ：Find the ratio of the leading coefficients, which are -3 and 5.

Step 3 ：$\frac{-3}{5} = -0.6$

Step 4 ：$\boxed{y = -\frac{3}{5}}$ or $\boxed{y = -0.6}$ is the horizontal asymptote of the given rational function.