{"status": "success", "data": {"description_md": "Two nonhorizontal, non vertical lines in the $xy$-coordinate plane intersect to form a $45^{\\circ}$ angle. One line has slope equal to $6$ times the slope of the other line. What is the greatest possible value of the product of the slopes of the two lines?\n\n$\\textbf{(A)}\\ \\frac16 \\qquad\\textbf{(B)}\\ \\frac23 \\qquad\\textbf{(C)}\\  \\frac32 \\qquad\\textbf{(D)}\\ 3 \\qquad\\textbf{(E)}\\ 6$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Two nonhorizontal, non vertical lines in the  <span class=\"katex--inline\">xy</span> -coordinate plane intersect to form a  <span class=\"katex--inline\">45^{\\circ}</span>  angle. One line has slope equal to  <span class=\"katex--inline\">6</span>  times the slope of the other line. What is the greatest possible value of the product of the slopes of the two lines?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac16 \\qquad\\textbf{(B)}\\ \\frac23 \\qquad\\textbf{(C)}\\  \\frac32 \\qquad\\textbf{(D)}\\ 3 \\qquad\\textbf{(E)}\\ 6</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "2020 AMC 12B Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc12B_p08", "prev": "/problem/20_amc12B_p06"}}