Jeannette and Keegan collect data about the length of a rope as knots are tied in it. The equation that fits their data is y = 102 - 6.3x, where x represents the number of knots and y represents the length of the rope in centimeters. Mitch had a piece of rope cut from the same source. Unfortunately he lost his data and can remember only that his rope was 47 cm long after he tied 3 knots. What equation describes Mitch's rope?

Question

SmokeyBrown · Answer

From Jeannette and Keegan's data, it seems like each knot takes away 6.3 centimeters of length away from the original length of the rope. This is seen in the equation
y = 102 - 6.3x, where x is the number of knots, and y is the length of the rope.

Mitch knows that his rope is 47 meters long *after* 3 knots are tied with it. Using the information already given, can you find the *original* length of the rope, from before the knots were tied? As a hint, remember that each knot takes away 6.3 centimeters, so to work backwards, try adding 6.3 for every knot in the rope.

Once you've figured that out, it should be simple to make an equation to represent Mitch's rope length.