An empty 5-gal water jug weighs 0.75 lb. with 3 c of water inside, the jug weighs 2.25 lb. which equation models the jug’s weight y when it contains x cups of water? y = –x + 3 y = 2x + 0.75 y = –0.167x + 2.25 y = 0.5x + 0.75

This models a linear equation. We can find the slope of a line from 2 points on the graph of the line. Even though we don't have the graph, we do have 2 points on the graph, x and y. x is the number of cups of water and y is the weight of the jug with that many cups of water in it. For our first coordinate, when there are no cups of water in the jug (x = 0), the weight of the jug is .75 (y = .75). So our first coordinate pair is (0, .75). For the next point, when there are 3 cups of water in the jug ( x = 3), the jug weighs 2.25 so the coordinate point is (3, 2.25). Now we can fit those into the slope formula to find the slope of the line.

and for us that looks like this:

which gives us a slope of 1.5/3 or .5. Now we pick a point, x and y, to sub into the slop-intercept form of the line to solve for b, the y-intercept.

.75=.5(0)+b and b = .75. Now we can rewrite the equation using the slope we found and the y-intercept we found, and that equation is y = .5x + .75, your last choice above.