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Let a and b be real numbers, where a < b, and let A = (a,a^2) and B = (b,b^2). The line \overline{AB} (meaning the unique line that contains the point A and the point B) has x-intercept (-3/2,0) and y-intercept (0,3). Find a and b. Express your answer as the ordered pair (a,b).

Guest Nov 16, 2014

Best Answer 

 #1
avatar+26399 
+10

slope = (3 - 0)/(0 - (-3/2)) or slope = 2

 

slope = (b2 - 3)/(b - 0) so  (b2 - 3)/b = 2

b2 - 3 = 2b

b2 - 2b - 3 = 0

(b + 1)(b - 3) = 0

so b = -1 or b = 3

Similarly we would find a = -1 or b = 3, but we are told a<b so a = -1 and b = 3

 

(-1, 3)

.

Alan  Nov 16, 2014
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1+0 Answers

 #1
avatar+26399 
+10
Best Answer

slope = (3 - 0)/(0 - (-3/2)) or slope = 2

 

slope = (b2 - 3)/(b - 0) so  (b2 - 3)/b = 2

b2 - 3 = 2b

b2 - 2b - 3 = 0

(b + 1)(b - 3) = 0

so b = -1 or b = 3

Similarly we would find a = -1 or b = 3, but we are told a<b so a = -1 and b = 3

 

(-1, 3)

.

Alan  Nov 16, 2014

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