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If the functional relationship is of the form y = cx where c is the constant of variation.

In graphical form, it is a straight line through the origin.

Q: How do you know that a direct variation is linear?

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I have recently been doing all these direct variation problems but not every linear relationship is a direct variation... But every direct variation is a linear relation!

YES...A direct variation is a linear relationship in which y-intercept is always 0.

no.

All direct variation graphs are linear and they all go through the origin.

The line doesn't go through the origin

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I have recently been doing all these direct variation problems but not every linear relationship is a direct variation... But every direct variation is a linear relation!

YES...A direct variation is a linear relationship in which y-intercept is always 0.

No.

no.

yes * * * * * No, it is not. In a direct variation, if one of the variables is 0, the other MUST also be 0. In a linear function, they will be the intercepts.

All direct variation graphs are linear and they all go through the origin.

Linear has a slope direct does not but both go through the orgin

Direct variation means that a linear function can be written as y = kx. The y-intercept must be (0, 0). The constant, k, is the slope.

if the line runs through the origin it is a direct variation no matter if it is increasing or decreasing

Y=1/x

The formula direct variation is xk=y, where k is the constant of variation.Direct variation functions always pass through the origin. Direct variation functions are linear functions (goes in a straight line), except that they pass through the origin. Regular linear functions don't pass through the origin. That is the only difference.

You then have a linear relationship, or a direct variation. A straight line through the origin.