<p>If b > 1, what is the slope of the line in the xy-plane the passes through the points ( b, b^2) and (b^2, b^4)?</p>
<p>(A) -b^2 + 5b</p>
<p>(B) -b^2 + b</p>
<p>(C) -b^2 - b</p>
<p>(D) b^2 - b</p>
<p>(E) b^2 + b</p>
<p>I believe that the answer is (E).
If b = 5, the points are (5, 25) and (25, 625) yielding a slope of 600/20 = 30
If b = 4, the points are (4, 16) and (16, 256) yielding a slope of 240/12 = 20
If b = 3, the points are (3, 9) and (9, 81) yielding a slope of 72/6 = 12</p>
<p>In each case, the slope is equal to b^2 + b</p>
<p>Slope = (b^4 - b^2)/(b^2 - b)</p>
<p>Factor b^2 from numerator, use difference of squares, cancel a bunch of stuff out, and you should obtain b^2 + b.</p>