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 = y = 3x - 1 Simplify your answer. Type an expression using x as the variable.)
Is the relationship a linear function?
O No
O yes
The relationship can be represented using the equation y = 3x - 1.
The relationship is a linear function because it can be represented by a straight line on a graph.
To represent the relationship using words:
Looking at the table, we can observe that the value of y is always one less than three times the value of x. Therefore, the relationship can be represented using words as "The value of y is one less than the quantity three times the value of x."
To represent the relationship using an equation:
We can see that the relationship between x and y can be represented by the equation y = 3x - 1. This equation shows that y is equal to three times x minus one.
To determine whether the relationship is a linear function:
A linear function is a function where the relationship between the independent variable (x) and the dependent variable (y) is linear, meaning that the rate of change is constant. In this case, the relationship between x and y can be represented by a linear equation y = 3x - 1. Since the equation is in the form y = mx + b, where m is the constant coefficient of x, we can conclude that the relationship is indeed a linear function.
Therefore, the answer is: Yes, the relationship is a linear function.
Yes, the relationship is a linear function.
The correct equation for the relationship is y = 3x - 1