Test of Essential Academic Skills (TEAS) ATI Mathematics Practice Test

Which graph description indicates a proportional relationship?

1. The graph has a slope of 2,500 and a y-intercept of 250.

2. The graph has a slope of 1,500 and a y-intercept of -150.

3. The graph has a slope of 2,000 and a y-intercept of 0.

4. The graph has a slope of -1,800 and a y-intercept of -100.

The correct answer is: The graph has a slope of 2,000 and a y-intercept of 0.

A proportional relationship is characterized by a constant ratio between variables, which means that the graph of this relationship is a straight line that passes through the origin (0,0). In other words, in a proportional relationship, when one variable is zero, the other variable must also be zero, leading to a y-intercept of 0. In the correct choice, the graph with a slope of 2,000 and a y-intercept of 0 demonstrates this characteristic. The slope indicates how steeply the line rises as one moves along the x-axis, while the y-intercept of 0 confirms that the line passes through the origin. This means for every increase in the x-value, the corresponding increase in the y-value maintains a constant ratio, which is a hallmark of proportionality. In contrast, the other choices each have a non-zero y-intercept. For instance, a slope of 2,500 with a y-intercept of 250 implies that even when the x-value is zero, the y-value will be 250, indicating that there is a starting point not at the origin. Similarly, the slopes and y-intercepts in the other options show that the lines do not start at the origin, thus failing to express a proportional