Look at this table:

Question

x y
–
1 7
0 3
1
–
1
2
–
5
3
–
9
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=

Answer 1

To determine whether the given data can be modeled by a linear function or an exponential function, we need to analyze the relationship between the x-values and the y-values.

Looking at the x-values, we can observe that for each increase in x by 1, there is a constant change in the y-values. This indicates that the data can be modeled using a linear function.

To find the slope (m) and y-intercept (b) in the equation y = mx + b, we can select any two sets of x and y values and calculate the slope using the formula:

m = (y2 - y1) / (x2 - x1)

Let's use the first two data points: (x1,y1) = (1, 7) and (x2, y2) = (0, 3)

m = (3 - 7) / (0 - 1) = -4 / -1 = 4

Now, let's substitute one of the data points into the equation and solve for the y-intercept (b). Let's use the first data point (1, 7):

7 = 4(1) + b
7 = 4 + b
b = 7 - 4
b = 3

Therefore, the linear function that models the data is:

y = 4x + 3

Answer 2

wrong its -4x+3

Answer 3

Apologies for the mistake. You are correct.

The linear function that models the data is:

y = -4x + 3