Quick questions on Reciprocal models and inverse variation for HSC Maths Standard 2

<!-- Diagram: reciprocal function rectangular hyperbola | reviewed 2026-05-21 --> <svg class="fig" viewBox="0 0 480 360" role="img" aria-labelledby="rec-t rec-d"> <title id="rec-t">Reciprocal function y equals k over x with two branches</title> <desc id="rec-d">A rectangular hyperbola with one branch in the first quadrant and a mirror branch in the third quadrant. Both axes are asymptotes; the curve approaches them but never touches.</desc> <line x1="40" y1="180" x2="460" y2="180" stroke="var(--ink)" stroke-width="0.9"/> <line x1="240" y1="30" x2="240" y2="335" stroke="var(--ink)" stroke-width="0.9"/> <text x="455" y="198" font-size="12" class="var">x</text> <text x="224" y="32" font-size="12" class="var">y</text> <text x="248" y="195" font-size="11" class="muted">0</text> <path d="M 252 50 Q 270 80 290 110 Q 320 150 360 168 Q 400 175 450 178" fill="none" stroke="var(--accent)" stroke-width="1.8"/> <path d="M 228 310 Q 210 280 190 250 Q 160 210 120 192 Q 80 185 30 182" fill="none" stroke="var(--accent)" stroke-width="1.8"/> <text x="350" y="115" font-size="12" font-weight="700" class="var">y = k ⁄ x, k &gt; 0</text> <text x="55" y="245" font-size="11" class="muted">third quadrant branch</text> <text x="380" y="200" font-size="11" class="muted">first quadrant branch</text> </svg>

When a table is given and you must decide whether it is inverse variation, multiply each pair.

In a physical problem $k$ is almost always positive. A negative $k$ usually means a slip in the $(x, y)$ pair.