Sumo wrestlers in japan are well known for their dedication, discipline, and very large bodies. a young sumo wrestler decides to go on a special high-protein diet to gain weight rapidly. after 4 months on this diet, his mass is 100 kilograms. after 14 months, his mass is 160 kilograms. let's assume that the sumo wrestler's mass changes at a constant rate while he is on this special diet.
what was the wrestler's mass in kilograms when he began his diet?

I prefer to think of this graphically. The weight is rising steadily so it is represented by a straight line (y = mx + c), where time is on the x-axis and mass is on the y-axis. We have been given two co-ordinates on this graph, (4, 100) and (14, 160). We need to find the equation of this graph.

First, realise that the gradient of a linear graph (m) is equal to the change in y over the change in x (Δy/Δx) - the change is just the difference between the two points:

Δy/Δx = (160-100)/(14-4) = 60/10 = 6

This gradient value can now be substituted into the general formula:

y = 6x + c

Next we need to find the constant value, or y-intercept (c). To do this, substitute in one of the sets of coordinates we have been given in the question, where the number of months is x and the mass is y (I'm going to use 4 months and 100kg). Then, solve for c:

y = 6x + c
100 = (6*4) + c
100 = 24 + c
c = 100 - 24 = 76

Now we know the full equation of the graph - y = 6x + 76. The question asks us to find the mass of the wrestler before putting on weight; this is represented by x=0 on the graph, because the x-axis represents time. Therefore, substitute x=0 into the equation to find the y value (the mass of the wrestler):

y = 6x + 76
y = (6*0) + 76 = 76kg

The initial mass of the wrestler was 76kg

I hope this helps