To find the equation for the linear function that models the relationship between X and Y, we can use the formula for the slope of a line:
m = (Y2 - Y1) / (X2 - X1)
Using the values from the table:
m = (56 - 38) / (6 - 4)
m = 18 / 2
m = 9
Now that we have the slope, we can use the point-slope form to find the equation of the line:
Y - Y1 = m(X - X1)
Using the point (4, 38):
Y - 38 = 9(X - 4)
Now simplify the equation:
Y - 38 = 9X - 36
Add 38 to both sides:
Y = 9X + 2
Therefore, the equation for the linear function that models the relationship between X and Y is Y = 9X + 2.