If y varies inversely as x, and y=10 as x=7, how do you find y for the x-value of 10?

Question

Hazel Anglin · Accepted Answer

undefined To find y for the x-value of 10, we can use the inverse variation equation. Inverse variation is represented by the equation y = k/x, where k is the constant of variation.

To find the value of k, we can use the given information that y = 10 when x = 7. Plugging these values into the equation, we get 10 = k/7.

To solve for k, we can multiply both sides of the equation by 7, resulting in 70 = k.

Now that we have the value of k, we can substitute it back into the inverse variation equation to find y for the x-value of 10.

Plugging in x = 10 and k = 70, we get y = 70/10. Simplifying this, we find that y = 7.

Therefore, when x = 10, y will be equal to 7.

Savannah Anderson · Answer

Inverse variation can be represented as:
# y = k/x# 
# k = y.x#  where #color(green)(k# is the constant  # x = 7 and y = 10#
so ,
# color(green)(k = 7 xx 10 = 70# Now, we have the value of #color(green)(k)# and #x = 10# , substituting these in the variation to find #color(red)(y#
#k= color(red)(y).x#  # color(red)(y )= k/x#  # color(red)(y = 70/10 = 7#  on observing the values  as the value of #x# decreases #y# increases and vice verse as they vary inversely.