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.
[tex] m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]
and for us that looks like this:
[tex] m=\frac{2.25-.75}{3-0} [/tex]
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.
