Suppose y varies inversely with x, how do you write an equation for the inverse variation if y = 8 when x = 1/2?

Question

Eva Adamson · Accepted Answer

Since it is an inverse variation it can be represented as:
# color(red)(y) = color(blue)(k/color(red)(x# , where #color(blue)(k# represents the constant term , #color(red)(x and y)# are the variables. Values for the variables are: 
#y=8# and #x=1/2# substituting these values :
# color(red)(y) = color(blue)(k/color(red)(x#
# color(red)(y.x) = color(blue)(k# # 1/2 . 8 = color(blue)(k) #
we get the constant as # color(blue)k = 4# # color(red)(y) = color(blue)(4/color(red)(x# # color(red)(x.y) = color(blue)(4#, represents the inverse variation in which constant is #4#.

Eli Assouline · Answer

undefined The equation for the inverse variation is y = k/x, where k is the constant of variation. To find the value of k, substitute the given values of y and x into the equation and solve for k. In this case, when y = 8 and x = 1/2, the equation becomes 8 = k/(1/2). Simplifying, we get 8 = 2k. Solving for k, we find k = 4. Therefore, the equation for the inverse variation is y = 4/x.