If two quantities are directly, which must be true of a graph showing relationships between them? Select all that apply.
A. The graph is a curve
B. The point on the graph are connected
C. The graph increases from left to right.
D.the points of the graph form a straight line.
E. The points of the graph must include the origin.
F. The points must all form equivalent ratios.
The thing is t here is no graph on the question
If y varies directly with x, then y = kx
for some constant value of k.
So, what kind of graph is that?
If two quantities are directly related, it means that they increase or decrease together at a constant rate. To determine what must be true of a graph showing relationships between these quantities, we can go through each option:
A. The graph is a curve: This is not necessarily true. A graph showing a direct relationship can be either a curve or a straight line, depending on the specific relationship between the quantities.
B. The points on the graph are connected: This is true. A graph showing a relationship between two quantities will have connected points to represent the continuous nature of the relationship.
C. The graph increases from left to right: This is true. In a direct relationship, as one quantity increases, the other quantity also increases. This means that the graph will have a positive slope and will trend upward from left to right.
D. The points of the graph form a straight line: This is true. In a direct relationship, the graph will have a linear shape, and the points will form a straight line. Therefore, this is a characteristic of a graph showing a direct relationship.
E. The points of the graph must include the origin: This is not necessarily true. Including the origin (the point (0, 0)) on the graph is not a requirement for a direct relationship between two quantities. It depends on the specific situation and the values of the quantities.
F. The points must all form equivalent ratios: This is not necessarily true. Equivalent ratios imply a constant ratio between the two quantities, which is not always the case in a direct relationship. Instead, in a direct relationship, the ratio between the two quantities remains constant, not necessarily equivalent for all points.
Therefore, the correct answers are B. The points on the graph are connected, C. The graph increases from left to right, and D. The points of the graph form a straight line.