x y
–
1
–
15
0
–
10
1
–
5
2 0
3 5
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
To determine if the data can be modeled using a linear or exponential function, let's first plot the points on a graph.
Plotting the points (x, y): (-1, 15), (0, 10), (1, 5), (2, 0), (3, 5), we get:
(1)
(15)*
‾‾
‾
(0)
(10)*
‾‾
‾
(-1)
(5)*
‾‾
‾
(-2)
(0)*
‾‾
‾
(-3)
(5)*
‾‾
‾
Observing the points on the graph, there is a linear relationship between x and y.
The line appears to have a negative slope, where the y-value decreases by 5 for every increase in the x-value by 1.
Thus, we can conclude that the data can be modeled using a linear function.
To find the equation of the line, let's find the slope (m) and y-intercept (b).
Slope (m) = change in y / change in x
m = (5 - 10) / (1 - 0) = -5/1 = -5
Using the point-slope form of a linear equation (y - y1 = m(x - x1)), we can choose any point on the line to substitute into the equation.
Let's use the point (1, 5):
y - 5 = -5(x - 1)
y - 5 = -5x + 5
y = -5x + 10
Therefore, the linear function that models the data is:
y = -5x + 10.