solve for k and you get k = xy.
k is the constant of variation.
it always remains the same.
what this means is, if you multiply x by some factor, you need to divide y by the same factor.
for example, let x = 4 and y = 8
the constant of variation is 4 * 8 = 32
if you multiply 4 by 2, then you have to divide 8 by 2.
you will get 8 * 4 = 32.
k has to stay the same.
that is what is meant by the constant of variation.
the formula for direct variation is y = k * x
solve for k to get k = y / x.
if you multiply y by some factor, you also have to multiply x by the same factor in order to keep k the same.
for example, let x = 4 and y = 8.
y / x = 2 = k
if you multiply y by 2, you have to multiply x by 2 as well in order to keep k constant.
you will get 16 / 8 = 2.
the same concept applies whether or not the values involved are positive or minus.
for example:
when x = -2, y = -6
k = -2 * -6 = 12
that's your constant of variation.
if x doubles, then y must be cut in half.
so when x becomes -4, y must becomes -3.
k = xy becomes -4 * -4 = 12.
k is constant.
what happens when x becomes 4.
4 * y = 12 in order to keep k constant.
solve for y to get y = 3.
when x = -2, y = -6
when x = -4, y = -3
when x = 4, y = 3
the constant of variation was always 12.
x * y = k
if x is multiplied by a factor, y must be divided by the same factor in order to keep k constant.
this can be seen graphically below.
your problem states:
if y = -6 when x = -2, find y when x = 5.
the formula is the same.
y = k / x
solve for k to get k = y * x.
when y = -6 and x = -2, you get k = 12
what happens when x = 5?
x * y = 12
when x = 5, the formula becomes 5 * y = 12
solve for y to get y = 12/5 = 2.4
-2 * -6 = 12
5 * 2.4 = 12
the constant of variation is always k.
you multiplied -2 by -2.5 to get 5.
you divided -6 by -2.5 to get 2.4.
inverse variation says that whatever you multiply x1 by to get x2, you need to divide y1 by to get y2.
in your problem, x1 was -2 and y1 was -6 while x2 was 5 and y2 was 2.4
you multiplied x1 by -2.5 to get x2 (-2 * -2.5 = 5)
you divided y1 by -2.5 to get y2 (-6 / -2.5 = 2.4)
this can be seen graphically below.
