The equation y = -1777x+27153 can be used to predict the number y of gun deaths in the United States x years after 20000, that is, x=0 corresponds to 2000, x=3 corresponds to 2003, x=5 corrresponds to 2005 and so on. Predict the number of gun deaths in 2005 and 2007. In what year will the number of gun deaths be 12937?

Here are my predictions
2005 number of deaths is 18,268
2007 number of deaths is 14714
in 2008 there will be 12937 deaths

is this correct?

Good job, I got the same

To predict the number of gun deaths in a given year using the equation y = -1777x + 27153, where x represents the number of years after 2000, we substitute the appropriate value of x into the equation.

1) For 2005 (x = 5), we substitute x = 5 into the equation:
y = -1777(5) + 27153
y = -8885 + 27153
y = 18268

So, the predicted number of gun deaths in 2005 is 18,268.

2) For 2007 (x = 7), we substitute x = 7 into the equation:
y = -1777(7) + 27153
y = -12439 + 27153
y = 14714

So, the predicted number of gun deaths in 2007 is 14,714.

3) To find the year in which the number of gun deaths will be 12,937, we can rearrange the equation:
y = -1777x + 27153
12,937 = -1777x + 27153
-1777x = 12,937 - 27153
-1777x = -15,216
x = -15,216 / -1777
x ≈ 8.57

Since x represents the number of years after 2000, we add this value to 2000 to find the year:
2000 + 8.57 ≈ 2008.57

Therefore, the number of gun deaths will be approximately 12,937 in the year 2008.

So, your predictions are correct:
- The predicted number of gun deaths in 2005 is 18,268.
- The predicted number of gun deaths in 2007 is 14,714.
- The predicted year for 12,937 gun deaths is 2008.