### Instruction: The graph of $y=\frac{5x^2-9}{3x^2+5x+2}$ has a horizontal asymptote at $y=a$.  What is $a$?### Response: I know that the horizontal asymptote of a rational function is the ratio of the leading coefficients of the numerator and the denominator, as long as the degrees of the numerator and the denominator are the same.
In this case, the degree of both the numerator and the denominator is 2, so I can use this rule.
The leading coefficient of the numerator is 5, and the leading coefficient of the denominator is 3, so the ratio is $\frac{5}{3}$.
Therefore, the horizontal asymptote is $y=\frac{5}{3}$, and $a=\frac{5}{3}$.