Which graphs display a directly proportional relationship? Check all that apply.

Question

On a coordinate plane, a line goes through points (0, 0) and (1, negative 3).
On a coordinate plane, a line goes through points (0, 1) and (1, 2).
On a coordinate plane, a line goes through points (0, 0) and (1, 3).
On a coordinate plane, a line goes through points (0, 0) and (2, 2).

Answer 1

A directly proportional relationship is characterized by a straight line that passes through the origin (0, 0) and maintains a constant ratio between the x and y values. In other words, if you double the x-value, the y-value must also double.

Let's analyze the graphs mentioned:

1. On a coordinate plane, a line goes through points (0, 0) and (1, -3).

   • This line passes through the origin, but since it has points where the y-values are negative, it does not represent a direct proportionality.

2. On a coordinate plane, a line goes through points (0, 1) and (1, 2).

   • This line does not pass through the origin (0, 1), so it is not directly proportional.

3. On a coordinate plane, a line goes through points (0, 0) and (1, 3).

   • This line passes through the origin and maintains a constant ratio, so it is directly proportional.

4. On a coordinate plane, a line goes through points (0, 0) and (2, 2).

   • This line passes through the origin and also maintains a constant ratio (the slope is 1), so it is directly proportional.

Based on this analysis, the graphs that display a directly proportional relationship are:

• The graph through points (0, 0) and (1, 3).
• The graph through points (0, 0) and (2, 2).