Fill in the blanks to complete the equation of the trend line that contains the points (1,77) and (3,40).

Elapsed time (T) 1, 2, 3, 4 Distance from finish line (D) 77, 55, 40, 17

1 answer

The equation of the trend line can be represented as:

D = mT + b

To find the values of m and b, we can use the given points (1,77) and (3,40).

Using the point (1,77):
77 = m(1) + b

Using the point (3,40):
40 = m(3) + b

We can now solve these two equations simultaneously to find the values of m and b.

From the equation 77 = m + b, we can rewrite it as b = 77 - m.

Substituting this value of b into the second equation, we get:
40 = m(3) + (77 - m)
40 = 3m + 77 - m
40 - 77 = 3m - m
-37 = 2m
m = -37/2
m = -18.5

Now substitute this value of m back into the equation for b:
b = 77 - m
b = 77 - (-18.5)
b = 77 + 18.5
b = 95.5

Therefore, the equation of the trend line is:
D = -18.5T + 95.5