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A line with slope m passing through (2,3) forms a triangle of area 12 with the coordinate axes.  What are the possible values of m?

 Jan 5, 2021
 #1
avatar+114361 
+1

I could only find one  value  for m ......there may  be others  !!!

 

(1/2) bh  =12

 

bh  =24

 

In one case,  the y intercept  must be  >  3

 

Note  that if  x= (4,0)  and y  = (0,6)   we have 

 

m =  6/-4  = -3/2

 

The equation of the  line through  (2,3)  is

 

y= (-3/2) (x - 2)  +  3

 

y =  (-3/2)x + 3 + 3

 

y= (-3/2)x + 6

 

And the area of the triangle is   (1/2) (6) (4)  =  12

 

Maybe someone else can  find other  possible  values  for  m  (if any more exist)

 

 

cool cool cool

 Jan 5, 2021
 #2
avatar+31514 
+1

I think there are three values:

(Just noticed that there should be a dot where the steepest line meets the x-axis!).

 Jan 5, 2021
edited by Alan  Jan 5, 2021

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