For the table to the right, represent the relationship using words, an equation, and a graph. Then determine whether the relationship is a linear function.
x y
0 -1
1 2
2 5
3 8
Represent the relationship using words. Choose the correct answer below.
A. The value of y is ten more than the cube of the quantity eight times the value of x. B. The value of y is the cube of the quantity eight plus the value of x. C. The value of y is one less than the quantity three times the value of x. D. The value of y is ten more than the quantity nine times the value of x. OE. The value of y is three times the value of x. OF. The value of y is the square of the quantity eight minus the value of x.
C. The value of y is one less than the quantity three times the value of x.
C. The value of y is one less than the quantity three times the value of x.
To represent the relationship using words, we need to analyze the given data in the table.
Looking at the values of x and y, we can see that as x increases by 1, y increases by 3. This means that for every unit increase in x, y increases by a constant amount of 3.
Now, let's analyze the answer choices:
A. The value of y is ten more than the cube of the quantity eight times the value of x. - This does not match our observed relationship where y increases by a constant amount.
B. The value of y is the cube of the quantity eight plus the value of x. - This is not consistent with the observed relationship.
C. The value of y is one less than the quantity three times the value of x. - This also does not match our observed relationship.
D. The value of y is ten more than the quantity nine times the value of x. - This does not match our observed relationship.
Therefore, none of the answer choices A, B, C, or D describe the relationship represented by the given table of values. Let's continue with the remaining answer choices:
E. The value of y is three times the value of x.
This relationship matches the observed pattern. For each unit increase in x, y increases by 3 (constant amount). Therefore, this answer choice is likely to represent the relationship in the table.
F. The value of y is the square of the quantity eight minus the value of x.
This equation does not represent the observed relationship where y increases by a constant amount for each unit increase in x.
Based on the analysis, the relationship described by answer choice E is the most suitable one. The relationship can be represented as "The value of y is three times the value of x."
Now, let's move on to representing the relationship using an equation and a graph.