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.
Represent the relationship using an equation. y = ___ Simplify your answer. Type an expression using x as the variable.)
y = 3x - 1
The equation representing the relationship is y = 3x - 1.
To represent the relationship using an equation, we can see that the value of y is always one less than three times the value of x. Therefore, the equation would be:
y = 3x - 1
This equation represents the relationship between x and y in the given table.
Next, let's determine whether the relationship is a linear function. A linear function is a function where the rate of change between any two points is constant. We can examine the differences in y-values for each pair of consecutive x-values in the table to check for a constant rate of change.
For the given table:
When x changes from 0 to 1, y changes from -1 to 2. The difference in y is 3.
When x changes from 1 to 2, y changes from 2 to 5. The difference in y is also 3.
When x changes from 2 to 3, y changes from 5 to 8. The difference in y is still 3.
As the differences in y-values stay constant for each pair of consecutive x-values, we can conclude that the relationship is a linear function.