Look at this table:
x y
–
2
–
23
–
1
–
15
0
–
7
1 1
2 9
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
Looking at the given table, we can see that as x increases by 1, y increases by a constant amount. Therefore, we can conclude that the given data can be modeled using a linear function.
To find the equation, let's find the slope (m) and y-intercept (b) using the given data points.
Using the points (1, 1) and (2, 9), we can find the slope:
m = (9 - 1) / (2 - 1) = 8
Now, using the point (1, 1) and the slope value, we can find the y-intercept:
1 = 8(1) + b
1 = 8 + b
b = 1 - 8
b = -7
Finally, putting the values of the slope and y-intercept into the linear equation form, we get:
y = 8x - 7