The table matches the equation ( y = 4x + 4 ) representing a linear function. Each x corresponds to a unique y, showing a constant rate of change, forming a linear graph. Thus, the relation is a function with a linear graph.
The table can be represented by the equation y = 4x + 4.
To verify this, let's check if the equation ( y = 4x + 4 ) holds true for the given values of x and y:
When x = 1, ( y = 4(1) + 4 = 8 ) (true)
When x = 2, ( y = 4(2) + 4 = 12 ) (true)
When x = 3, ( y = 4(3) + 4 = 16 ) (true)
When x = 4, ( y = 4(4) + 4 = 20 ) (true)
Therefore, the statement is true: the table can be represented by the equation ( y = 4x + 4 ).
The graph of the function is nonlinear.
From the equation ( y = 4x + 4 ), the relationship between x and y is linear because it follows a straight line. Thus, this statement is false. The graph is linear.
The relation is a function.
A function has a unique y-value for each x-value. In this case, each x-value corresponds to a unique y-value. Hence, this statement is true. The relation is a function.
The rate of change is not constant.
Looking at the differences in y-values as x increases by 1 each time:
( 12 - 8 = 4 )
( 16 - 12 = 4 )
( 20 - 16 = 4 )
The rate of change between consecutive x-values is constant (4). Therefore, this statement is false. The rate of change is constant.
The graph of the function is linear.
As per the equation ( y = 4x + 4 ), the relationship between x and y forms a straight line. Thus, this statement is true. The graph of the function is linear.
Therefore, the true statements based on the given information are:
The table can be represented by the equation ( y = 4x + 4 ).
The relation is a function.
The graph of the function is linear.
complete the question
A number of squares are connected in a row to form a rectangle. The table shows the relationship between the number of squares, x, and the perimeter, y, of the rectangles they form.
| Number of Squares (x) | Perimeter (y) |
|---|---|
| 1 | 8 |
| 2 | 12 |
| 3 | 16 |
| 4 | 20 |
Based on this information, select all of the following statements that are true:
The table can be represented by the equation y = 4x + 4.
The graph of the function is nonlinear.
The relation is a function.
The rate of change is not constant.
The graph of the function is linear.