A 12-inch ruler is divided into three parts. The largest part is three times as a long as the smallest. The middle-sized part is
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-2x+14 is the same as 14 - 2x
Let's say you started off with $14. If you want to buy a soda worth $2, then you have 14-2 = 12 dollars left. If you buy two sodas, then you spend 2*2 = 4 dollars with 14-4 = 10 dollars left.
In general, buying x sodas will cost you 2*x dollars and you have 14 - 2x dollars left over. The x is simply a placeholder for a whole number. For example, if x = 3, then...
14 - 2x = 14 - 2*3 = 14 - 6 = 8
meaning buying 3 sodas cost you $6 and you have $8 left over.
If y is the amount left over, then we can say y = 14 - 2x which is equivalent to y = -2x+14
note: graphing this equation will go through the two points (0,14) and (7,0) as shown in the image below. A graph is handy to help see various points on the line. Each point represents the amount of sodas you can buy (x) and the amount left over in your pocket (y). Keep in mind that neither x nor y can be negative, so it only makes sense to restrict the graph.
