Look at this table:
x y
–
1 9.5
0 2.5
1
–
4.5
2
–
11.5
3
–
18.5
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
To determine if the function is linear or exponential, we need to check if the values of y change at a constant rate.
Looking at the table, we can see that as x increases by 1, the value of y changes by a constant amount of 7.
This indicates that the function is linear.
To find the linear equation, we can use the two points given in the table: (0, 2.5) and (1, 9.5).
First, calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
m = (9.5 - 2.5) / (1 - 0)
m = 7
Next, we need to find the y-intercept (b). We can use one of the points, for example, (0, 2.5).
Using the slope-intercept form of a linear equation, y = mx + b, we can substitute the values:
2.5 = 7(0) + b
2.5 = b
So the linear function that models the data is:
y = 7x + 2.5