|
Question 1063646: Here's another problem I have no clue how to do.
The point P (3,2) is on line L. The sum of the x and y intercepts of line L is 12. Find all possible equations for line L in standard form.
Found 2 solutions by Fombitz, rothauserc:
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! Start with the general equation of a line,
So you know (3,2) is on the line,
and the x intercept is,
and the y intercept is,
and their sum,
Combining with the previous equation,
Two solutions:
So then,
So the solution line looks like,
and
So,
So this solution line looks like,
Answer by rothauserc(4718)  (Show Source):
You can put this solution on YOUR website! The standard form of a line is
:
Ax + By = C, where A, B, C are integers and A > 0
:
if x = 0, then y = C/B, this is the y intercept
:
if y = 0, then x = C/A, this is the x intercept
:
For line L, we know that
:
1) C/A + C/B = 12
:
using point (3,2)
:
2) 3A + 2B = C
:
We have three points on Line L - (3, 2), (C/A, 0), (0, C/B)
:
slope(m) = (y2 - y1) / (x2 - x1) = ( 3 - 0) / (2 - C/B) = 3 / (2 - C/B)
slope(m) = (3 - C/A) / 2
:
set both equations for m equal to each other
:
(3 - C/A) / 2 = 3 / (2 - C/B)
:
from equation 1) we know that C/A = 12 - C/B
:
let C/B = k, then
:
6 = (3 - 12 + k) * ( 2 - k)
:
6 = (-9 + k) * (2 - k) = -18 +11k -k^2
:
k^2 -11k +24 = 0
:
(k - 8) * (k - 3) = 0
:
there are two possible values to consider
:
C/B = 8
C/B = 3
:
C/A + 8 = 12, C/A = 4 and C = 8B
4A = 8B
A = 2B
2Bx + Bx = 8B
2x +y = 8
:
C/A + 3 = 12, C/A = 9, C = 3B
9A = 3B
A = B/3
Bx/3 + By = 3B
x + 3y = 9
:
************
2x + y = 8
x + 3y = 9
************
:
|
|
|
| |
