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Select all of the ordered pairs \((x,y)\) that are solutions to the linear equation \(2x+3y=6\).
\((0,2)\)
\((0,6)\)
\((2,3)\)
\((3,\text-2)\)
\((3,0)\)
\((6,\text-2)\)
The graph shows the relationship between the number of comic books Priya buys at the store and the amount of money in dollars that Priya has left after buying the comic books.
\(y = 1.5x\)
\(2x + 3y = 7\)
\(x - y = 4\)
\(3x = \frac y2\)
\((14, 21)\), \((2,3)\), \((8,12)\)
\((\text-3, \text-7)\), \((0, \text-4)\), \((\text-1,\text-5)\)
\(\left(\frac 18, \frac78\right), \left(\frac 12,\frac 12\right), \left(\frac 14, \frac 34\right)\)
\(\left(1, 1\frac23\right), \left(\text-1,3\right), \left(0, 2\frac13\right)\)
A container of fuel empties at a rate of 5 gallons per second. A graph representing this situation is drawn in the coordinate plane, where \(x\) is the number of seconds that have passed since the container started emptying, and \(y\) is the amount of fuel remaining in the container.
Will the slope of the line representing this situation have a positive, negative, or zero slope? Explain your reasoning.
A sandwich shop charges a delivery fee to bring lunch to an office building. One office pays 33 dollars for 4 turkey sandwiches including the delivery fee. Another office pays 61 dollars for 8 turkey sandwiches including the delivery fee.