Which statement is always true?
A.
A linear relationship is proportional.]]]]]]]]]]]]]]]]]]]
B.
A linear relationship is non-proportional.
C.
A proportional relationship contains the point
D.
A non-proportional relationship has a constant rate of change.
C. A proportional relationship contains the point (0,0)
Trust me I got it right, or don’t and get it wrong, your choice.
what was the answer?
To determine which statement is always true, let's review the definitions of each term mentioned.
1. A linear relationship represents a straight line on a graph, where the relationship between two variables can be expressed by an equation in the form y = mx + b, where m is the slope of the line and b is the y-intercept.
2. Proportional relationship refers to a linear relationship where the ratio between two variables remains constant. In other words, if one variable doubles, the other variable also doubles in a proportional relationship.
3. Non-proportional relationship refers to a linear relationship that does not have a constant ratio between the two variables. This means that doubling one variable does not necessarily result in the other variable also doubling.
Now, let's evaluate each statement:
A. "A linear relationship is proportional." This statement is NOT always true because not all linear relationships are proportional. Some linear relationships are non-proportional, where the ratio between the two variables changes.
B. "A linear relationship is non-proportional." This statement is NOT always true because there are linear relationships that are proportional.
C. "A proportional relationship contains the point (0,0)." This statement is NOT always true either because although many proportional relationships contain the point (0,0), it is possible for proportional relationships to exist without this particular point.
D. "A non-proportional relationship has a constant rate of change." This statement is always true. In a non-proportional relationship, the rate of change (slope) between the two variables is not constant. It means that the ratio of the change in y to the change in x is different at different points along the line.
Therefore, the statement that is always true is D. "A non-proportional relationship has a constant rate of change."