If y varies directly as x, and y=42 as x=6, how do you find y for the x-value 3?

Question

Nathan Axel · Accepted Answer

undefined To find y for the x-value 3, we can use the concept of direct variation. Since y varies directly as x, we can set up a proportion using the given values.

First, we can write the direct variation equation as y = kx, where k is the constant of variation.

To find the value of k, we can use the given information that y = 42 when x = 6. Plugging these values into the equation, we get 42 = k * 6.

Solving for k, we divide both sides of the equation by 6, giving us k = 7.

Now that we have the value of k, we can use it to find y for the x-value 3. Plugging x = 3 into the direct variation equation, we get y = 7 * 3.

Simplifying, we find that y = 21.

Therefore, when x = 3, y is equal to 21.

Isaiah Anthony · Answer

Direct variation can be represented as:
# x/y = k# 
where #color(green)(k# is the constant  # x = 6 and y = 42#
so substituting : 
# 6/42 = k#
# color(green)(k = 1/7# Now, we have the value of #color(green)(k)# and #x = 3# , substituting these in the variation to find #y#
# x/color(red)(y) = k#  # 3/color(red)(y )= 1/7#  By cross multiplying we get 
# color(red)(y = 21#  on observing the values  # color(red)(y# is always #7# times #x# , as the constant #color(green)(k = 7#