Look at this table:
x y
1
–
2
2
–
11
3
–
20
4
–
29
5
–
38
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
To find the pattern in the data, we can see that the y-values are increasing by 9 each time the x-value increases by 1. This suggests that the relationship could be modeled by a linear function.
Using the formula y = mx + b, where m is the slope and b is the y-intercept, we can find the equation.
Let's find the slope (m) by taking any two points from the table. Let's choose the points (1, -) and (2, -11).
m = (y2 - y1) / (x2 - x1)
m = (-11 - (-)) / (2 - 1)
m = (-11 + ) / 1
m = -11 +
Now, let's find the value of b by substituting the slope (m) and one of the points into the equation.
Using the point (1, -) and m = , we have:
- = (1)(-) + b
- = - + b
b = - -
Therefore, the linear function that models the data is y = (x - )