SAT数学题求解释In the xy-coordinate plane, the graph of x = y*y -4 intersects line l at (0, p) and (5, t). What is the greatest possible value of the slope of l?（求大神救救我TAT,这题是肿么回事.）

Question

SAT数学题求解释
In the xy-coordinate plane, the graph of x = y*y -4 intersects line l at (0, p) and (5, t). What is the
greatest possible value of the slope of l?（求大神救救我TAT,这题是肿么回事.）

Answer 1

这是求斜率的最大值问题,可设此直线l的方程为y=kx+b,此直线又与曲线x=y^2-4交于(0,p)和(5,t),则可得：0=p^2-4,5=t^2-4,解得p=±2,t=±3,另外此两点在直线上,故可得：
p=b,5k+b=t,即k=(t-p)/5,故k的最大值是(3+2)/5=1