Look at this table:
x y
–
5
–
45
–
4
–
38
–
3
–
31
–
2
–
24
–
1
–
17
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 function or an exponential function, we can plot the points on a graph and analyze the trend.
x y
–5 –
45
–4 –
38
–3 –
31
–2 –
24
–1 –
17
To create a graph from the given data, we plot the x and y values as points:
(-5, 45)
(-4, 38)
(-3, 31)
(-2, 24)
(-1, 17)
Plotting these points and connecting them with a line gives us a diagonal line that decreases as x increases.
Since the line is straight and not curving, we can conclude that the data can be modeled by a linear function.
To find the equation of the line, we can calculate the slope (m) and y-intercept (b) by using any two points from the graph:
m = (y2 - y1) / (x2 - x1)
m = (38 - 17) / (-4 - (-1))
m = 21 / (-3)
m = -7
We can choose the point (-1, 17), then plug in the values for m and the point into the y = mx + b equation to solve for b:
17 = -7(-1) + b
17 = 7 + b
b = 17 - 7
b = 10
Therefore, the linear function that models the data is:
y = -7x + 10