Set A shows a linear relationship with "Y equals 25X plus 75," while Set B lacks a consistent pattern, refuting the claim of a linear relationship in statement 2.
In Set A, the relationship between X and Y is indeed linear, as evidenced by the consistent increase in Y by 25 units for each increment of X by 1. This linear relationship is accurately captured by the equation "Y equals 25X plus 75." The slope of 25 reflects the constant rate of change in Y concerning X, and the intercept of 75 represents the Y-value when X is 0.
Contrastingly, Set B does not exhibit a clear linear relationship. The values of Y in Set B do not follow a consistent pattern as X increases. The proposed equation "Y equals 25X plus 50" inaccurately suggests a constant slope of 25, which is not evident in the data. The relationship in Set B is more complex, with varying changes in Y for each unit increase in X, making it non-linear.
In summary, Set A demonstrates a linear relationship described by "Y equals 25X plus 75," while Set B lacks a consistent pattern indicative of a linear relationship, making statement 2 false.
The probable question may be:
"Given two data sets, Set A and Set B, with corresponding values for X and Y as follows:
**Set A:**
X Y
-1 50
0 60
1 75
2 100
3 125
**Set B:**
X Y
-1 0.60
0 75
1 15
2 75
3 375
Which of the following statements is true regarding the relationship between X and Y in each set?"
1. In Set A, the relationship between X and Y is linear, and it can be expressed by the equation \(Y = 25X + 75\). This is evident from the consistent increase in Y by 25 units for each increment of X by 1.
2. In Set B, the relationship between X and Y is linear, and it can be described by the equation \(Y = 25X + 50\). This statement is false because Set B does not exhibit a clear linear relationship; the values of Y do not follow a consistent pattern as X increases.
3. Set A and Set B both show a quadratic relationship between X and Y. This statement is false as Set A demonstrates a linear relationship, and Set B lacks a consistent pattern indicative of a quadratic relationship.
4. Set A and Set B both have identical slopes in their relationships between X and Y. This statement is false as the slopes differ; Set A has a slope of 25, while Set B does not exhibit a constant slope.