Question

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

Answer 1

a. 3.25 lb

Explanation:

Answer 2

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.

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

and for us that looks like this:

`m=(2.25-.75)/(3-0)`

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.