In 1920, the record for a certain race was 45.8 sec. In 1970, it was 44.8 sec. Let R(t)=the record in the race and t= the number of years since 1920.
a)Find a linear function that fits the data.
b)Use the function in (a) to predict the record in 2003 and in 2006.
c)Find the year when the record will be 43.82 sec.

Question

anonymous · Answer

(0, 45.8) and (50,44,8) are the two points.  Have you tried finding the slope of these?

anonymous · Answer

(50,44.8)

anonymous · Answer

No i havent. i looked at the question and got confused.

anonymous · Answer

Try that, the y-intercept is 45.8 use the y = mx+b

anonymous · Answer

that gets you part (a)

anonymous · Answer

substitute in 83 and 86 to get 2003 and 2006

anonymous · Answer

I always find it irritating when they say "linear function" because it sounds like it might be a linear transformation which is altogether different than a first degree polynomial

anonymous · Answer

Yeah , that's why im really confused.

anonymous · Answer

Can someone help me step by step?

anonymous · Answer

$$m=\frac{y_2-y_1}{x_2-x_1}=\frac{44.8 - 45.8}{1970-1920}$$$$R(t) = \frac{44.8 - 45.8}{1970-1920}t + 45.8$$