The general form of a linear equation is y = mx + b, where y is the dependent variable (total number of bears), x is the independent variable (year), m is the slope, and b is the y-intercept.
Let's assume that the number of bears in the park increased by a constant rate each year. Let's denote the number of bears in the park during Year 1 as Y1.
We are given that the number of bears in the park during Year 3 is 50:
Y3 = 50
We can write a linear equation in the form of y = mx + b using the given data:
Y3 = m(3) + b
50 = 3m + b
We need another piece of information to solve for m and b. Let's use the fact that the total number of bears in the park during Year 2 is 40:
Y2 = 40
We can write another linear equation using this information:
Y2 = m(2) + b
40 = 2m + b
Now we have a system of two equations:
50 = 3m + b
40 = 2m + b
We can solve this system of equations to find the values of m and b. Subtracting the second equation from the first:
10 = m
Now that we have found the value of m, we can substitute it back into either of the original equations to solve for b. Using the first equation:
50 = 3(10) + b
50 = 30 + b
b = 20
Therefore, the linear equation representing the number of bears in the park each year is Y = 10x + 20. To find out how many bears were in the park during Year 1, plug x = 1 into the equation:
Y1 = 10(1) + 20
Y1 = 10 + 20
Y1 = 30
Therefore, there were 30 bears in the park during Year 1.
The total number of bears in the park during Year 3 is 50. Write and solve a linear equation to determine how many bears were in the park during Year 1. Note that this answer will not be the same as the answer you got in part
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