Question

Writing a linear equation. Write an equation in slope intercept form of the line that is segment bisected of both AB and CD

Answer 1

9514 1404 393

Answer:

  y = -8x +3

Step-by-step explanation:

We don't need the midpoint formula to find the midpoints. We can count grid squares.

B is 2 up from A, and right 4. So, the midpoint of AB is 1 up and right 2 from A, or point (0, 3).

D is down 4 from C, and right 6. So, the midpoint of CD is down 2 and right 3 from C, or point (1, -5).

The vertical difference between the first midpoint and the second is -8. The horizontal difference is +1, so the slope of the line between the midpoints is ...

  m = rise/run = -8/1 = -8

The first midpoint is the y-intercept of the line, so the equation of the line is ...

  y = -8x +3

_____

If you want to use all of the appropriate formulas, you can. The midpoint formula is ...

  M = ((x1, y1) +(x2, y2))/2 = (x1 +x2, y1 +y2)/2

  M = (A +B)/2 = ((-2, 2) +(2, 4))/2 = (0, 6)/2 = (0, 3)

  N = (C +D)/2 = ((-2, -3) +(4, -7))/2 = (2, -10)/2 = (1, -5)

The slope of line MN is ...

  m = (y2 -y1)/(x2 -x1) = (-5 -3)/(1 -0) = -8/1 = -8

The point-slope equation is ...

  y -y1 = m(x -x1)

  y -3 = -8(x -0)

  y = -8x +3 . . . . . .  add 3 to put into slope-intercept form