SOLUTION: Find the equation of all lines passing through the point (6, -1) for which the product of their x- and y-intercepts is 3

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Question 1155733: Find the equation of all lines passing through the point (6, -1) for which the
product of their x- and y-intercepts is 3

Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20849) (Show Source):
You can put this solution on YOUR website!

given:
lines passing through the point (, )
the
product of their x- and y-intercepts is

if the product of their x- and y-intercepts is , one intercept must be and other must be
let’s find out which one is and which one is

x-intercept at:(,)
y-intercept at:(,)
then a slope of the line that passes through intercepts is:

plug it in equation of the line:

......use given point to calculate

-> if then y-intercept is
=> x-intercept must be
and =>=>
your equation will be:

Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

The solution by the other tutor is incomplete; there are two lines that satisfy the given conditions.

In her solution, she assumes that, since the product of the two intercepts is 3, one of the must be 3 and the other must be 1. That is not true.

Let the intercepts be (a,0) and (0,b).

The equation of the line is y = mx+b. We know
(1)
(2) (6,-1) is on the line, so

(3)

Simplify (2) and substitute (3):

(4)

Substitute (4) in (3):

or

ANSWERS:

b=-1/2 and ab=3 means a = -6; the intercepts are (-6,0) and (0,-1/2); the equation is y = (-1/12)x-1/2

b = 1 and ab=3 means a=3; the intercepts are (3,0) and (0,1); the equation is y = (-1/3)x+1

A graph....