What is the constant of variation, k, of the direct variation, y = kx, through (5, 8)?
k = -8/5, k= - 5/8, k= 5/8, k= 8/5

Solution:

A relationship between two variables m and n represent a direct variation if it can be expressed in the form n/m = ⍺ or n = ⍺ m

Where, ⍺ is constant of variant.

Now, given a point (5, 8)

Substitute x = 5 and y = 8 in y = kx

8 = k(5)

k = 8/5

Example:

Find the constant variation of the k, of the direct variation y = kx, through (7, 9)

Solution:

A relationship between two variables m and n represent a direct variation if it can be expressed in the form n/m = ⍺ or n = ⍺ m where, ⍺ is constant of variant.

Now, given a point (7, 9) substitute x = 7 and y = 9 in y = kx.

9 = k(7)

K = 9/7

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What is the constant of variation, k, of the direct variation, y = kx, through (5, 8)?

Summary:

The constant of variation, k, of the direct variation, y = kx, through (5, 8) is k = 8/5.