Project - would you please check my answers?

I am working on a project and my linear equation came out to be:
y = 1502.9x - 2847386

This project is about waste and recycling so the equation came from a table that gave a few years and the tons of waste in each of those years.

1) We have to state the slope, so I am saying that the slope is 1502.9 which means that on average there are 1502.9 tons of waste each year. Is this correct?
2) Does the equation have a y-intercept? I am saying that my y-intercept is (0, -2857386).
The question asks what does this mean in terms of the context of the problem.
I am thinking that since our years begin in 1990, it means that that is how much is already present in the landfill? But I'm not entirely sure because I don't understand the negative sign -- please help!

3) Does your equation have an x-intercept? If so, solve to find the x-intercept. I'm really unclear about this one because to me it would seem there would not be an x-intercept since this would be the beginning of time, or, you can't have no trash.

#1 ok

#2 the y-intercept is negative. If the records started in 1990, then that is just a back-projection on the slope of the line. Not really much meaning in this context.
#3 the x-intercept is where y=0 (x=1894). That could be when records started, but it is more likely that they started keeping records sometime after that year, like 1990. The line is just a best-fit for the records on hand. It is very likely that before 1990 the rate of growth was much slower, causing the graph to flatten out to the left.

So then if I solved my equation, I would get something like x = 1901, so would I say then that I DID have an x intercept?

every sloping line has an x- and a y-intercept!

Shart si etisbew siht

I'd be happy to help you check your answers!

1) You are correct in stating that the slope is 1502.9. The slope represents the rate of change of the dependent variable (in this case, the tons of waste) with respect to the independent variable (the years). So, on average, there is an increase of 1502.9 tons of waste each year.

2) The equation does have a y-intercept. In this case, the y-intercept represents the value of y when x is 0. Your y-intercept is (-2857386). In the context of waste and recycling, this means that when the year is 1990 (or x = 0), there are already -2857386 tons of waste present. The negative sign indicates that the value is below zero, suggesting that there was already a substantial amount of waste present before the start of the recorded data.

It's important to note that the interpretation of y-intercepts in real-world contexts can sometimes be tricky, and it's always good to consider the specific details of the problem.

3) You are correct in suspecting that there may not be an x-intercept in this case. The x-intercept represents the value of x when y equals zero. In the context of waste and recycling, this would imply a year where there is no waste. However, since waste is continuously generated, it would be unlikely to have an x-intercept.

In summary, your answers for 1) and 2) are correct, and 3) is also correct in stating that there may not be an x-intercept in this context. Well done on your project!