Look at this table:
x y
–1 –13
0 –3
1 7
2 17
3 27
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
The data in the table can be modeled by a linear function. To find the equation of the linear function (y = mx + b), we need to find the values of m and b.
First, let's find the slope (m) using the formula:
m = (change in y) / (change in x)
From the table, we see that the change in y as x increases by 1 is 10 (from -3 to 7, or from 7 to 17, etc.), and the change in x is 1. Therefore, the slope (m) is found by dividing the change in y by the change in x:
m = 10 / 1
m = 10
Now, let's find the y-intercept (b) by substituting the values of x and y from any pair of points in the table into the equation y = mx + b and solving for b. Let's use the point (0, -3):
-3 = 10(0) + b
-3 = b
Therefore, b is -3.
Finally, we can write the equation of the linear function that models the data as y = 10x - 3.