A graph indicates direct variation if it is a straight line and it passes through (0,0) the origin.
If the graph does not pass through the origin (0,0) is does not represent direct variation.
In a table of values, look at the relationship between x and y. If you use the same number everytime to multiply x to get a 7, that's direct variation.
In a linear function, if there is no y-intercept, that is direct variation. If there is a y-intercept, that's not direct variation. A linear equation y = mx + b with no y-intercept becomes y = mx which has the same structure as the general equation for direct variation, y = kx.
A graph indicates inverse variation if it is a curved line that approaches but never touches the x- and y- axes.
The general equation for inverse variation is y = k/x.
In direct variation, the constant of variation k multiplies the x.
In inverse variation, the constant of variation k is divided by x.
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