# find possible slopes of line passing thru (4,3) so portion of line in first quadrant

• May 23rd 2012, 03:44 PM
sluggerbroth
find possible slopes of line passing thru (4,3) so portion of line in first quadrant
...forms triangle of area 27 wit positive coordinate axes.

book has answer -3/2 or -3/8

i found first answeer but not second???
• May 23rd 2012, 04:23 PM
skeeter
Re: find possible slopes of line passing thru (4,3) so portion of line in first quadr
Quote:

Originally Posted by sluggerbroth
...forms triangle of area 27 wit positive coordinate axes.

book has answer -3/2 or -3/8

i found first answeer but not second???

let $x_i$ and $y_i$ represent the positive x and y intercepts of the line

$\frac{x_i \cdot y_i}{2} = 27 \implies x_i \cdot y_i = 54$

slope of the line is $m = -\frac{y_i}{x_i}$

$y = mx + b$

$3 = -\frac{y_i}{x_i} \cdot 4 + y_i$

$3 = -y_i\left(\frac{4}{x_i} -1\right)$

$3 = -\frac{54}{x_i} \left(\frac{4}{x_i} -1\right)$

$3 = -\frac{216}{x_i^2} + \frac{54}{x_i}$

$3x_i^2 = -216 + 54x_i$

$3x_i^2 - 54x_i + 216 = 0$

$x_i^2 - 18x_i + 72 = 0$

$(x_i - 6)(x_i - 12) = 0$

$x_i = 6 \implies y_i = 9$ ... $m = -\frac{9}{6} = -\frac{3}{2}$

$x_i = 12 \implies y_i = 4.5$ ... $m = -\frac{4.5}{12} = -\frac{9}{24} = -\frac{3}{8}$

also, in future please post entire problem within the post ... not part in the title, rest in the post. thanks.
• May 23rd 2012, 04:47 PM
sluggerbroth
Re: find possible slopes of line passing thru (4,3) so portion of line in first quadr
how do know negative slope? ie m=-y/x??
• May 23rd 2012, 05:39 PM
skeeter
Re: find possible slopes of line passing thru (4,3) so portion of line in first quadr
Quote:

Originally Posted by sluggerbroth
how do know negative slope? ie m=-y/x??

Quote:

...forms triangle of area 27 wit positive coordinate axes
I always make a sketch before working on a problem ... I'm sure that you do, also, right?