MathDB
two slopes

Source: 2020 AMC 12B #7

February 6, 2020
analytic geometrygraphing linesslopeAMC 12 B2020 AMC 12B2020 AMCAMC

Problem Statement

Two nonhorizontal, non vertical lines in the xyxy-coordinate plane intersect to form a 4545^{\circ} angle. One line has slope equal to 66 times the slope of the other line. What is the greatest possible value of the product of the slopes of the two lines?
<spanclass=latexbold>(A)</span> 16<spanclass=latexbold>(B)</span> 23<spanclass=latexbold>(C)</span> 32<spanclass=latexbold>(D)</span> 3<spanclass=latexbold>(E)</span> 6<span class='latex-bold'>(A)</span>\ \frac16 \qquad<span class='latex-bold'>(B)</span>\ \frac23 \qquad<span class='latex-bold'>(C)</span>\ \frac32 \qquad<span class='latex-bold'>(D)</span>\ 3 \qquad<span class='latex-bold'>(E)</span>\ 6