Which values from the set {0, 1/2 , 2.5, 4} make the inequality 8g < 4 true?

only 0

Step-by-step explanation:

8g < 4 simplifies to g < 4/8, i.e., g < 1/2

only 0 is smaller than 1/2

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!