Look at the table:
X y
-1 -7.5
0 0.9
1 9.3
2 17.7
3 26.1
Write a linear function (y = mx + b) or an exponential function (y = a(b)^x) that models the data.
y = blank
To determine whether the data can be modeled by a linear function or an exponential function, let's calculate the differences between consecutive y-values:
1st difference:
0.9 - (-7.5) = 8.4
9.3 - 0.9 = 8.4
17.7 - 9.3 = 8.4
26.1 - 17.7 = 8.4
The differences between consecutive y-values are all the same, which indicates that the data can be modeled by a linear function.
Now, let's find the equation of the linear function.
Using the point-slope form of a linear function (y - y₁ = m(x - x₁)) and the coordinates (0, 0.9):
y - 0.9 = m(x - 0)
Since x₁ is 0, the equation simplifies to:
y - 0.9 = mx
Rearranging the equation to the slope-intercept form (y = mx + b):
y = mx + 0.9
Hence, the linear function that models the data is:
y = mx + 0.9