Which linear function shows a direct variation?

D. Graph D

Step-by-step explanation:D. Graph D

Step-by-step explanation:

We know that, 'Direct Variation or Directly Proportional' is relationship between two variables where one is a constant multiple of the other.

That is, if one variable changes, the other variable also changes in proportion to the first variable.

The general form of 'Direct Variation' is y = kx, where k is a constant i.e. it does not have a y-intercept.

Now, according to our options, we see that the figures of A,B,C are the graphs of the straight lines given by y =-2x+2 , y=2x+2, y=-2x+2 respectively.

Each of these three equations have y-intercept, therefore cannot be the equations of a direct proportion.

Now, in option D, the figure is the graph of straight line y = -x and has no y-intercept.

Hence, the linear function in Graph D shows a direct proportion.

the formula of a slope:

we have the points (-2, 7) and (2, 3). substitute: