How do you determine the constant of variation k in the direct variation equation y = kx when given the point (5, 8)?

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To determine the constant of variation k in the direct variation equation y = kx, you can use the coordinates of the point provided. In this case, the point is (5, 8), where:

  • x = 5
  • y = 8

Now, substitute these values into the equation:

y = kx

Replacing y and x with their respective values gives:

8 = k * 5

To isolate k, divide both sides of the equation by 5:

k = 8 / 5

Simplifying this gives:

k = 1.6

Thus, the constant of variation k for the direct variation through the point (5, 8) is 1.6.

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