Posted by Knights on Saturday, March 9, 2013 at 5:28pm.
A line with slope 6 bisects the area of a unit square with vertices (1,0), (0,0) , (1,1), and (0,1). What is the yintercept of this line?
I tried putting one point where the line intersects the square as (y,1), and the other as (x,0), and the y intercept as (0,a). Then, I tried using the slope to figure out the variables. The only problem is that I don't have enough equations. Help?

Please help analytic geometry  Damon, Saturday, March 9, 2013 at 5:52pm
I would say it hit the square at (a, 0) and at (b , 1)
Area of trapezoid on left = (a+b)/2(1) = (a+b)/2
Area of trapezoid on right = [(1b)+(1a)]/2
= (2  a  b)/2
if those areas are equal then
a + b = 2  a  b
or as we could see from the sketch
a + b = 1
Now the slope of 6
b = a + (1/6)
so
a + a + 1/6 = 1
2 a = 5/6
a = 5/12
then
b = 5/12 + 1/6 = 7/12
NOW you have a problem I am sure you can do
find c in y = 6 x + c
It goes through (5/12 , 0)
0 = 5/2 + c
so
c = 5/2
y = 6 x  5/2
for y axis intercept, x = 0
y = 5/2

Please help analytic geometry  Steve, Saturday, March 9, 2013 at 9:46pm
You know the line is y=6(xa) so it intercepts the xaxis at (0,a), and the line y=1 at x=(1+6a)/6 = 1/6 + a
So, the left half of the figure is a trapezoid with height 1 and bases a and (1/6 + a)
So, if that has area 1/2,
1(a+a+1/6)/2 = 1/2
a = 5/12
so, y = 6(x5/12)
y = 6x  5/2

Or, consider the point C=(1/2,1/2), the center of the square. A vertical line through C would cut the square in half.
Since we want a line of slope 6, so y increases 6 for every increase in 1 by x. If the line passes through C, then if it leans to the right 1/12 at y=1 and to the left 1/12 at y=0, it will still cut the square in half. So, we have the line through (5/12,0) and (7/12,1).
y = 6x  5/2

Please help analytic geometry  Knights, Saturday, March 9, 2013 at 9:49pm
THANKS A LOT!
Answer This Question
Related Questions
 math  i have more than one question so if u no any of the answers please tell ...
 geometry  Use the information given to determine the equation of each line. a. ...
 geometry  14.Use the information given to determine the equation of each line. ...
 math  I am a little lost on my homework can someone help me with these problems...
 math and slopes  Help. Determine the slope of the line. The line whose equation...
 Math/Algebra do u know how to do slope intercept?  The following problems are ...
 math  1. The xintercept of a line is 3. The yintercept of a line is 6. What ...
 Math(Please help)  Write an equation of the line satisfying the given condition...
 Math  A line 'l' intersects line 'm' at point A at 45 degree angle. B and C are...
 Algebra  Can you please help me with this problem: The xintercept of a line ...
More Related Questions