For each equation, determine whether it shows a direct variation (that is, shows directly proportional variables).

Question

If it does, find the constant of variation and write it in simplest form.

16y=8x k=

8x-4y=0 k=

Answer 1

For the equation 16y = 8x, it shows a direct variation because the variables y and x are directly proportional.

To find the constant of variation (k), we can rewrite the equation in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

16y = 8x
Divide both sides by 16:
y = (8/16)x
Simplify the fraction:
y = (1/2)x

The constant of variation (k) is 1/2.

For the equation 8x - 4y = 0, it also shows a direct variation because the coefficient of x (8) is the same as the coefficient of y (-4), but with opposite signs.

To find the constant of variation (k), we can isolate y by rearranging the equation:

8x - 4y = 0
Subtract 8x from both sides:
-4y = -8x
Divide both sides by -4:
y = (8/4)x
Simplify the fraction:
y = 2x

The constant of variation (k) is 2.