Do the data in the table represent a linear function? if so, write a rule for the function X= -2,-1,0,1,2
Y= -7, 1,8,17,25
A. yes; y= 8x + 9
B. yes ; y = 8x +8
C. yes ; y = 1/8x+8
D. no***
C 1/8x +8
I'm sorry your answer is correct zero.
I mean no
The answer is d no
To determine if the data in the table represents a linear function, we need to check if there is a constant rate of change between the values of x and y.
First, let's calculate the differences between consecutive y-values and their corresponding x-values:
The difference between y-values: 1 - (-7) = 8 - 1 = 17 - 8 = 25 - 17 = 8
The difference between x-values: (-1) - (-2) = 0 - (-1) = 1 - 0 = 2 - 1 = 1
Since the differences between the y-values are constant and equal to 8, and the differences between the x-values are constant and equal to 1, we can conclude that the data represents a linear function.
Now, let's find the slope (m) of the linear function:
m = (change in y) / (change in x) = 8 / 1 = 8
Using the point-slope form of a linear equation (y - y₁ = m(x - x₁)), we can choose any point from the table, such as (-2, -7), and substitute the values into the equation:
y - (-7) = 8(x - (-2))
y + 7 = 8(x + 2)
y + 7 = 8x + 16
Now, we can rewrite the equation in slope-intercept form (y = mx + b) by isolating y:
y = 8x + 16 - 7
y = 8x + 9
Therefore, the rule for the linear function represented by the data in the table is y = 8x + 9.
The correct answer is A. Yes; y = 8x + 9.