The graph represents distance traveled varying directly with time. what would be the distance traveled after 9 hours? select one: a. 450 miles b. 360 miles c. 400 miles d. 40 miles

The direct variation equation is . That means, in words, that y varies directly as x. k is the constant of variation. We can pick a coordinate point on the graph to solve for this constant, then use that constant along with the x value of 9 hours to find the distance we could travel in that 9 hours. This is kind of like a way to write a linear equation that you could use as a model. I picked the point (2.5, 100) since the line goes right through that point. Fitting those points into the direct variation equation we get . If we solve for k we get that k = 40. Now since time is an x value and distance is a y value, we are looking to solve for y when x = 9. We have the k, so here's the equation: . We multiply both sides by 9 to solve for y. y = 360. Choice b from above. There you go!

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