Question

Determine whether the equation represents a direct variation. If it​ does, find the constant of variation.

6y = 5x - 1

Answer 1

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Part 1
Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x = 18.

y = 7 when x = 6

Answer 2

you sure?

Answer 3

that was incorrect

Answer 4

To determine if the equation represents a direct variation, we need to check if it can be written in the form y = kx, where k is the constant of variation.

Let's rearrange the equation to isolate y:

6y = 5x - 1

Divide both sides by 6:

y = (5x - 1)/6

We can see that the equation cannot be written in the form y = kx. Therefore, it does not represent a direct variation.

Answer 5

To write a direct variation equation, we use the form y = kx, where k is the constant of variation.

Given that y = 7 when x = 6, we can substitute these values into the equation to solve for k:

7 = k * 6

Divide both sides by 6:

k = 7/6

Now that we have the value of k, we can write the direct variation equation:

y = (7/6)x

To find the value of y when x = 18, we substitute this value into the equation:

y = (7/6) * 18
y = 7 * 3
y = 21

Therefore, when x = 18, y = 21.

Answer 6

Apologies for the mistake in my previous response. Let's correct it:

To write a direct variation equation, we use the form y = kx, where k is the constant of variation.

Given that y = 7 when x = 6, we can substitute these values into the equation to find k:

7 = k * 6

Divide both sides by 6:

k = 7/6

Now that we have the value of k, we can write the direct variation equation:

y = (7/6)x

To find the value of y when x = 18, we substitute this value into the equation:

y = (7/6) * 18
y = 21

Therefore, when x = 18, y = 21.

Answer 7

Apologies for the confusion. Let's correct it:

Given that y varies directly with x, 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 substitute the given values into the equation:

7 = k * 6

Divide both sides by 6:

k = 7/6

Now that we have the value of k, we can write the direct variation equation:

y = (7/6)x

To find the value of y when x = 18, we substitute this value into the equation:

y = (7/6) * 18

y = 21

Therefore, when x = 18, y = 21.