Please help analytic geometry

posted by .

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 y-intercept 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 -

    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 = [(1-b)+(1-a)]/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 -

    You know the line is y=6(x-a) so it intercepts the x-axis 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(x-5/12)
    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 -

    THANKS A LOT!

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    I am a little lost on my homework can someone help me with these problems please! With a GM MasterCard, 5% of the amount charged is credited toward a rebate on the purchase of a new car. Express the R as a function of the amount charged …
  2. math and slopes

    Help. Determine the slope of the line. The line whose equation is 3x-2y=8 Solve for y by putting y on one side and everything else on the other. -2y=8-3x. Multiply by -1. 2y = 3x -8 and divide by 2 y=(3/2)x -8/2 or y= (3/2)x -4 The …
  3. Math/Algebra do u know how to do slope intercept?

    The following problems are in slope,point slope, and slope intercept forms of a line. Could you check these thanks. Find the slope intercept form of a line that passes through these two points (-4,4) and (2,1) Answer: y= -1/2x-2 Find …
  4. math

    1. The x-intercept of a line is -3. The y-intercept of a line is 6. What is the slope of the line?
  5. math

    i have more than one question so if u no any of the answers please tell me 1.) write the point-slope form of the equation of the line with slope -2 passing through the point ( -5, -9). 2.) write the point-slope form of an equation …
  6. geometry

    14.Use the information given to determine the equation of each line. a. the slope of the line is 4/3 and its y-intercept is -2 b.the line perpendicular to the line y=-2x+5 and passing through the point (-2,6)
  7. geometry

    Use the information given to determine the equation of each line. a. the slope of the line is 4/3 and its y-intercept is -2 b.the line perpendicular to the line y=-2x+5 and passing through the point (-2,6)
  8. Math(Please help)

    Write an equation of the line satisfying the given condition. a) x intercept = 3 y intercept=-2 I am really not sure how to start here. b) vertical line containing (5,-1) Would it be y=5x-1?
  9. geometry

    I would love for someone to check my work on the seven problems that I did. I would be eternally grateful. I am going to list my problems and answers. Even if you only want to check one of them, that would be great. 1. Write an equation …
  10. Algebra

    Can you please help me with this problem: The x-intercept of a line has a value of -3/2 and a y intercept of 3. Another line has a slope that is three times the slope of the first line and has a y-intercept that is 28 more than the …

More Similar Questions