Question

Which linear graph represents a proportional relationship?
a graph of a line that passes through the points 0 comma 0 and 1 comma negative 3
a graph of a line that passes through the points 0 comma 2 and 1 comma 2
a graph of a line that passes through the points 0 comma negative 3 and 2 comma 1
a graph of a line that passes through the points 0 comma negative 1 and 2 comma negative 2

Answer 1

A proportional relationship is represented by a linear graph that passes through the origin (0, 0). This means that the line must have a y-intercept of 0.

Let's evaluate the options:

1. **A graph of a line that passes through the points (0, 0) and (1, -3)**: This line starts at the origin, but since the second point is not above the x-axis, it does not represent a proportional relationship. The slope is negative, and the y-values are not proportional to the x-values.

2. **A graph of a line that passes through the points (0, 2) and (1, 2)**: This line is horizontal and doesn't pass through the origin. It represents a constant value (y = 2), not a proportional relationship.

3. **A graph of a line that passes through the points (0, -3) and (2, 1)**: This line does not pass through the origin (it starts at -3 on the y-axis), and therefore does not represent a proportional relationship.

4. **A graph of a line that passes through the points (0, -1) and (2, -2)**: This line also does not pass through the origin (it starts at -1 on the y-axis) and does not represent a proportional relationship.

None of the options provided represent a proportional relationship since none of them pass through the origin (0,0).