Look at this table:
x y
–
1
–
3
0
–
5
1
–
7
2
–
9
3
–
11
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
For the given data, it can be observed that as the value of x increases by 1, the corresponding value of y decreases by 2. This indicates a linear relationship between x and y.
To find the linear function that models the data, we need to determine the values of m and b in the equation y = mx + b.
Looking at the data, we can see that when x = 0, y = -5. This gives us one point on the line: (0, -5).
Now, we can use another point to find the slope (m) of the line. Let's choose the point (2, -9):
m = (change in y) / (change in x)
m = (-9 - (-5)) / (2 - 0)
m = (-9 + 5) / 2
m = -4 / 2
m = -2
Now that we have the slope (m), we can substitute it and the coordinates of one point (0, -5) into the equation y = mx + b to solve for b:
-5 = -2(0) + b
-5 = b
Therefore, the linear function that models the data is:
y = -2x - 5