Look at the table and choose “true” or “false”.
X Y
1 1
2 4
3 9
4 16
5 25
This table shows a proportional relationship. T/F
This table shows a linear relationship. T/F
This table represents a function. T/F
This table shows a constant rate of change. T/F
This table shows an increasing relationship. T/F
False (not proportional)
True (linear)
True (represents a function)
False (not constant rate of change)
True (increasing relationship)
is it perorational?
No, the table does not show a proportional relationship.
To determine the answers, we need to understand the definitions of a proportional relationship, a linear relationship, a function, a constant rate of change, and an increasing relationship.
1. Proportional relationship: A relationship where the ratio between two variables remains constant. To check if the table shows a proportional relationship, we need to check if the ratio between the values in the Y column to the corresponding values in the X column is consistent. Let's calculate the ratios:
- Ratio 1: Y(1) / X(1) = 1 / 1 = 1
- Ratio 2: Y(2) / X(2) = 4 / 2 = 2
- Ratio 3: Y(3) / X(3) = 9 / 3 = 3
- Ratio 4: Y(4) / X(4) = 16 / 4 = 4
- Ratio 5: Y(5) / X(5) = 25 / 5 = 5
Since the ratios are not consistent, the table does not show a proportional relationship. The answer is False.
2. Linear relationship: A relationship where the graph between two variables forms a straight line. To check if the table shows a linear relationship, we can plot the points (X, Y) and see if they form a straight line. Plotting the points, we can see that they form a perfect straight line. Therefore, the table shows a linear relationship. The answer is True.
3. Function: A relation where each input (X) has exactly one output (Y). To check if the table represents a function, we need to make sure that each X value has a unique Y value. In this case, each X value has a unique Y value, so the table represents a function. The answer is True.
4. Constant rate of change: A consistent change in the dependent variable (Y) for every unit change in the independent variable (X). To check if the table shows a constant rate of change, we need to see if the difference between the Y-values for consecutive X-values remains the same. Let's calculate the differences:
- Difference 1: Y(2) - Y(1) = 4 - 1 = 3
- Difference 2: Y(3) - Y(2) = 9 - 4 = 5
- Difference 3: Y(4) - Y(3) = 16 - 9 = 7
- Difference 4: Y(5) - Y(4) = 25 - 16 = 9
Since the differences are not consistent, the table does not show a constant rate of change. The answer is False.
5. Increasing relationship: A relationship where the values of the dependent variable (Y) increase as the values of the independent variable (X) increase. Looking at the table, we can see that as X increases, Y also increases. Therefore, the table shows an increasing relationship. The answer is True.
In summary:
- This table shows a proportional relationship: False
- This table shows a linear relationship: True
- This table represents a function: True
- This table shows a constant rate of change: False
- This table shows an increasing relationship: True