No, not every relationship whose graph passes through the origin represents direct variation. Direct variation specifically means that the relationship can be expressed in the form ( y = kx ), where ( k ) is a non-zero constant. While a graph passing through the origin indicates a proportional relationship, it can also represent other types of relationships, such as quadratic or polynomial functions, if they contain additional terms. Therefore, the key characteristic of direct variation is the constant ratio between ( y ) and ( x ), not just the point of intersection at the origin.
The line doesn't go through the origin
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.
All direct variation graphs are linear and they all go through the origin.
Graphs of direct variation pass through the origin so the y-intercept would be 0.
Constant variation is a relationship between two variables where one is a fixed multiple of the other. The graph of such a relationship is a straight line through the origin.
if the line runs through the origin it is a direct variation no matter if it is increasing or decreasing
You then have a linear relationship, or a direct variation. A straight line through the origin.
The line doesn't go through the origin
Inverse variation does not pass through the origin, however direct variation always passes through the origin.
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.
yes, a graph of a direct variation must pass through the origin because direct variation is always in form of y=mx where x and y are variables and m is a constant.
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.
All direct variation graphs are linear and they all go through the origin.
Graphs of direct variation pass through the origin so the y-intercept would be 0.
It is a straight line passing through the origin.
It is a straight line passing through the origin.
For a direct variation, y=kx where k is the constant of variation if x =0 then y=0 and the graph of y=kx passes through the origin. -Indiana Prentice Hall Algebra 2 Text Book.