In the x-y coordinate plane, the graph of #x=y^2-4# intersects line l at #(0,p)# and #(5,t)#? What is the greatest possible value of the slope of l?

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Answer 1 · 2017-11-19T20:53:57

#m = 1#

Given:

Points #(0,p)# and #(5,t)# lie on the curve #x = y^2-4#

The slope of a line through the points is:

#m = (t-p)/(5-0)#

#m = (t-p)/5#

When we solve for t and p, we discover that both have two possible values as follows:

#0 = p^2-4# and #5 = t^2-4#

#p^2=4# and #t^2=9#

#p=+-2# and #t=+-3#

The greatest value will occur when, t is positive and p is negative:

#m = (3- (-2))/5#

#m = 5/5#

#m = 1#