look at this table:
x -10 -9 -8 -7 -6
y 78.57 69.89 61.21 52.53 43.85
Write a linear function (y = mx + b) or an exponential function (y=a(b)^x) that models the data
To determine whether the data can be modeled by a linear function or an exponential function, we need to look for patterns or relationships between the x and y values. Let's first calculate the differences between consecutive y-values:
Difference between -10 and -9 = 69.89 - 78.57 = -8.68
Difference between -9 and -8 = 61.21 - 69.89 = -8.68
Difference between -8 and -7 = 52.53 - 61.21 = -8.68
Difference between -7 and -6 = 43.85 - 52.53 = -8.68
As we can see, the differences between consecutive y-values are constant (-8.68). This suggests that the data could be modeled by a linear function.
To find the equation of a linear function in the form y = mx + b, we need to find the values of m (slope) and b (y-intercept).
We can calculate the slope (m) using the formula:
m = (y2 - y1)/(x2 - x1)
Let's use the first two points (-10, 78.57) and (-9, 69.89) to calculate the slope:
m = (69.89 - 78.57)/(-9 - (-10))
= -8.68/1
= -8.68
Now we can find the y-intercept (b) by substituting one of the points (-10, 78.57) along with the slope into the equation y = mx + b:
78.57 = (-8.68)(-10) + b
78.57 = 86.8 + b
b = 78.57 - 86.8
b = -8.23
Therefore, the linear function that models the data is:
y = -8.68x - 8.23