Look at this table:
x y
3
–
24
4
–
33
5
–
42
6
–
51
7
–
60
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
To find the equation that models the data, we need to find the relationship between x and y.
By looking at the table, we can see that as x increases by 1, y increases by 9. This indicates a linear relationship between x and y.
Using the formula for a linear function (y = mx + b), where m is the slope and b is the y-intercept, we can find the equation:
To find the slope (m):
m = (change in y)/(change in x) = (y2 - y1)/(x2 - x1) = (33 - 24)/(4 - 3) = 9/1 = 9
Now, we can substitute the slope into the equation:
y = 9x + b
To find the y-intercept (b), we can use any point from the table. Let's use the point (3, 24):
24 = 9(3) + b
24 = 27 + b
24 - 27 = b
-3 = b
Now, substitute the y-intercept into the equation:
y = 9x - 3
So the linear function that models the data is y = 9x - 3.