Context: For $y = \dfrac{45 - x}{ax + b}$ with positive constants $a$ and $b$, the task is to identify where this graph crosses the $x$-axis.

Answer: D) $(45, 0)$

Why? Crossing the $x$-axis means $y = 0$, and a quotient is $0$ exactly when its numerator is $0$ while its denominator is not. So $45 - x = 0$ gives $x = 45$, and $45a + b > 0$ keeps the function defined there.

Traps:

• A) $\left(-\dfrac{b}{a}, 0\right)$ -> solving $ax + b = 0$ finds where the function is undefined, not where its value is zero.
• B) $\left(0, \dfrac{45}{b}\right)$ -> substituting $x = 0$ returns the $y$-intercept, which answers a different question.
• C) $(0, -45)$ -> an $x$-coordinate of $0$ places this on the $y$-axis, and the value ignores the denominator entirely.