Question

I am looking at an olympic event that has happened every 4 years (except for when the olympics didn't happen because of the wars). I found a line of best fit for this data and it is y = -0.0101x + 29.809

The questions are a) Does your graph have a y-intercept? If so, what is the meaning of the y-intercept? If not, why?

I'm confused here, because the y-intercept is where the line would cross the y axis. We had to have data reaching back to 1912 (I'm not sure when the Olympics actually started), but I'm thinking that the line wouldn't cross the y axis unless it was 0 years, and the Olympics didn't start in year 0, so would my answer be no, there is no y-intercept because the Olympics didn't start in year 0 of the world?

But, if I wanted to find the y-intercept, would I insert 0 in for x into my equation, so y = 0.0101(0) + 29.809 and this would mean that in year 0 the time was 29.809 seconds?

So, a little confused as to if there is or is not a y-intercept.

and b) Does your graph have an x-intercept? If so, what is the meaning of the x-intercept? If not, why?
Well, the x-intercept is where the line crosses the x axis and that couldn't happen because then the event would be done in 0 seconds which obviously would not make any sense. Is that correct?

But, if I wanted to find out the x-intercept, I would insert 0 for y, so,
0 = -0.0101x + 29.809 and solve, the answer being 2951 which would mean in year 2951 the event is run in 0 seconds.

So I guess I'm confused by which answer I should put to those questions - the x and y intercepts don't make sense but I guess they COULD happen (well, not the x one, but the y if the Olympics started in year 0)

Answer 1

Seems that your line of best fit might not be best one (just joking lol). Anyways, from the equation that I see, it seems correct (both your y and x values for the intercepts), however, you are right about the value of 2951 = x being 0, as that would be impossible, (unless that event no longer exist). This value of y at x = 2951 shows that extrapolating the values that you have is not reliable (as the further the values are extrapolated, the less reliable these values become). Thus this value of 0 at 2951 can be attributed to these unreliable predictions. For the y-values, it be again caused by (if you interpolate your values) unreliable values being predicted by the line of best fit.

SIDE NOTE: please check your values and graph again as it can also calculation or inputting values error.

P.S: The Olympics (MODERN) started in 1896. As the ANCIENT Olympics they started way before 0 A.D (around 776 B.C.)

Answer 2

So my answer for part a is:
a) yes it does have a y-intercept (proceed to solve for y-intercept)
Meaning ==> read post above to give you some insight.
b) yes it does have a x-intercept (proceed to solve for x-intercept)
Meaning ==> read post above.

P.S. I hope this helped! Please reply if have any other questions.