Emily has 2/8 cups of sugar. Amelia has 1/2 cup of sugar. How many cups of sugar do they have altogether? Provide your answer in simplest form.

Given
Profit on every sandwich (x) is $2
Profit on every wrap (y) is $3
Profit last month is $1470
Profit next month is $1593

Find
A: put the equation for last month's profit in slope-intercept form; identify the slope and y-intercept
B: describe in complete sentences how to graph this equation
C: write the equation in function notation. Explain what the function represents.
D: Graph the function; label the intercepts.
E: Explain how the graphs of the functions for last month's profit and next month's profit are similar and different.
F: (graph not supplied) Explain how you would write the equation for the graph.

Solution
A: To put a standard form equation into slope-intercept form, solve for y. Do that by subtracting the x-term and dividing by the coefficient of y.
  2x +3y = 1470
  3y = -2x +1470 . . . . subtract the x-term
  y = (-2/3)x + 490
    slope = -2/3
    y-intercept = 490

B: Graph this function by plotting the y-intercept on the y-axis. That point is (0, 490). Then find another point that is 2 units down for every 3 units to the right. Draw a line through that point and the y-intercept. (One such point is the x-intercept, (735, 0).)

C: The equation of part B can be written in function notation by replacing "y" with "f(x)".
  f(x) = (-2/3)x + 490
The function represents the number of wraps that must be sold in order to have a profit of $1470 as a function of the number of sandwiches sold.

D: See the attached graph.

E: The graph of the function for next month's profit is a line parallel to the one for the last month's profit. The slopes of the two graphs are the same. The intercepts of the two graphs are different.

F: You can write the equation using the slope-intercept form, provided that the y-intercept is given or can be read from the graph. Likewise, if the x-intercept is given, you can write the equation using that:
  y = (-2/3)(x - 'x-intercept')
Otherwise, you would have to determine a couple of points on the graph and use the 2-point form of the equation for a line to write the equation. For points (x1, y1) and (x2, y2), that form is
  y -y1 = (y2 -y1)/(x2 -x1)·(x -x1)