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)

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.)

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.

For your first question, whether the graph has a y-intercept, you are correct in your reasoning. The y-intercept is the point where the line crosses the y-axis, which occurs when the value of x is 0. In this context, x represents the years since the Olympics started. Since the Olympics didn't start at year 0, there is no meaningful y-intercept in this case. So the answer would be no, there is no y-intercept.

However, if you still want to find the y-intercept mathematically, you would indeed substitute 0 for x in the equation y = -0.0101x + 29.809. This would give you y = 0.0101(0) + 29.809, which simplifies to y = 29.809. Therefore, the y-intercept in this case would represent the predicted time (in seconds) for the event in the year the Olympics started (assuming it started at year 0), which is 29.809 seconds.

For your second question, whether the graph has an x-intercept, your reasoning is also correct. The x-intercept is the point where the line crosses the x-axis, which represents the year where the time for the event is 0 seconds. Since it wouldn't make sense for the event to be completed in 0 seconds, there is no meaningful x-intercept in this case. So the answer would be no, there is no x-intercept.

However, if you still want to find the x-intercept mathematically, you would substitute 0 for y in the equation -0.0101x + 29.809 = 0. By solving this equation, you would find the value of x where the time is predicted to be 0 seconds. In this case, x would be approximately 2951, which means that according to the line of best fit, the event would be completed in 0 seconds around the year 2951.

In summary, given the context of the Olympic event and the equation of the line of best fit, it is reasonable to conclude that there is no meaningful y-intercept (since the Olympics didn't start at year 0) and no meaningful x-intercept (since the event wouldn't be completed in 0 seconds). However, mathematically, you can still calculate these intercepts, but their interpretations might not be meaningful in this specific scenario.