Question

What is the constant of variation for a function that is a direct variation and whose graph passes through the point (5,82)?

Answer 1

Answer:

For a direct variation equation passing through

(

x

,

y

)

=

(

5

,

−

6

)

we have

−

6

=

m

⋅

(

5

)

→

m

=

−

6

5

and the direct variation equation is

y

=

(

−

6

5

)

x

which you might re-write as

5

y

=

−

6

x

Answer 2

The constant of variation for a function that is a direct variation and whose graph passes through the point (5,82) is 16.4

For a graph with x and y-axis, we can say that y is directly proportional to "x" since it is a direct variation.

If y is directly proportional to x, this is expressed as:

y = kx

k is the required constant of variation.

Since the graph passes through the point (5,82), this shows that x = 5 and y = 82

Substituting into the formula:

82 = 5k

k = 82/5

k = 16.4

Hence the constant of variation for a function that is a direct variation and whose graph passes through the point (5,82) is 16.4

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