Look at this table:
x y
–
9 48.8
–
8 43.1
–
7 37.4
–
6 31.7
–
5 26
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
To determine if the data can be modeled by a linear or exponential function, we need to examine the relationship between the x and y values. Looking at the given table, it appears that as the x values decrease, the y values also decrease. This suggests that the data can be modeled by a linear function.
To find the linear function that models the data, we need to find the slope (m) and y-intercept (b). We can do this by finding the equation of the line that passes through two points from the table.
Let's take the points (-9, 48.8) and (-8, 43.1):
Slope (m) = (y2 - y1) / (x2 - x1)
= (43.1 - 48.8) / (-8 - (-9))
= -5.7 / 1
= -5.7
Using the point-slope form of a linear function (y - y1 = m(x - x1)) with the point (-9, 48.8):
y - 48.8 = -5.7(x - (-9))
y - 48.8 = -5.7(x + 9)
y - 48.8 = -5.7x - 51.3
Rearranging the equation to the slope-intercept form (y = mx + b):
y = -5.7x - 2.5
Therefore, the linear function that models the data is y = -5.7x - 2.5.