Look at this table:
x y
–
4 38
–
3 31
–
2 24
–
1 17
0 10
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
To determine whether the given data can be modeled by a linear or exponential function, let's first examine the relationship between the values of x and y.
When we observe the data, we can see that as x decreases by 1, y decreases by a consistent value. This indicates a linear relationship between x and y.
To find the equation of the linear function, we need to determine the values of m and b in y = mx + b.
Looking at the y-values in the table, we can see that when x = -1, y = 17. Therefore, b = 17.
Since the relationship is linear and the change in y is consistent as x decreases by 1, we can calculate the slope (m) using two points: (0, 10) and (-1, 17).
m = (change in y) / (change in x)
= (10 - 17) / (0 - (-1))
= -7 / 1
= -7
Now we have m = -7 and b = 17, so the equation of the linear function is:
y = -7x + 17