I have seen examples of this but the examples are not helping me solve it or set it up as a y=mx +b
The equation y= -1777x + 27,153 can be used to predict the number of gun deaths in the U.S. x years after 2000, x=0 corresponds to 2000 x=3 corresponds to 2003, x=5 corresponds to 2005 Predict the number of gun deaths in 2005 and 2008. In what year will gun deaths be 11,160 ?
2005:
2008:
When will gun deaths reach 11,160 in a year:
Y = -1777 (5) + 27153 = -8885 + 27153=
18268.
Y = -1777(8) + 27153 = 12937.
Y = -1777X + 27153 = 11160
-1777X = -15993
X = 9 = yr. 2009
thank you Henry. I love the story problems but this one was a bit much.
To use the equation y = mx + b, we need to first understand the values of the variables in the given equation.
In the equation y = -1777x + 27,153:
- "y" represents the predicted number of gun deaths.
- "x" represents the number of years after 2000.
- "-1777" is the slope of the line, which indicates the rate of change (decrease) in gun deaths per year.
- "27,153" is the y-intercept, which represents the predicted number of gun deaths in the year 2000 (when x = 0).
Now let's use this equation to find the number of gun deaths in 2005 and 2008:
1. For 2005 (x = 5):
Substitute x = 5 into the equation:
y = -1777(5) + 27,153
y = -8,885 + 27,153
y = 18,268
Therefore, the predicted number of gun deaths in 2005 is 18,268.
2. For 2008 (x = 8):
Substitute x = 8 into the equation:
y = -1777(8) + 27,153
y = -14,216 + 27,153
y = 12,937
Therefore, the predicted number of gun deaths in 2008 is 12,937.
Now let's find out in what year the number of gun deaths will reach 11,160:
Substitute y = 11,160 into the equation:
11,160 = -1777x + 27,153
Rearrange the equation to solve for x:
-1777x = 11,160 - 27,153
-1777x = -15,993
Divide both sides by -1777 to isolate x:
x = -15,993 / -1777
x ≈ 9
Therefore, the number of gun deaths will reach 11,160 approximately 9 years after 2000. Since x = 0 corresponds to the year 2000, it means gun deaths will reach 11,160 in the year 2009.
To summarize:
- The predicted number of gun deaths in 2005 is 18,268.
- The predicted number of gun deaths in 2008 is 12,937.
- Gun deaths will reach 11,160 in the year 2009.