Two points (a,b) and (c,d) are shown on a graph. Which of the following equations correctly represents the slope of the line that passes through these points.

Rationale

(d-b)/(c-a)

The slope of a line that passes through two points \((a, b)\) and \((c, d)\) is calculated by the formula \(\frac{d-b}{c-a}\). This formula captures the change in the \(y\) values divided by the change in the \(x\) values, which accurately represents the slope of the line.

A ((b-d)/(a-c)) YOUR ANSWER

This option incorrectly computes the slope by reversing the \(y\) values and the \(x\) values in the formula. It calculates the change in \(y\) as \(b - d\) instead of \(d - b\), and the change in \(x\) as \(a - c\) instead of \(c - a\). This results in a negative slope when the actual slope should be positive for points where \(c > a\).

B ((d-b)/(c-a)) CORRECT

This choice correctly represents the slope of the line between the two points by using the formula \(\frac{d-b}{c-a}\). It calculates the change in \(y\) as \(d - b\), and the change in \(x\) as \(c - a\), which gives the correct slope between the points on the graph.

C ((b-d)/(c-a)) YOUR ANSWER

This option incorrectly computes the slope by reversing the \(y\) values while keeping the \(x\) values correct. It uses \(b - d\) instead of \(d - b\), which would yield a negative slope when the actual slope could be positive depending on the relative positions of the points.

D ((d-b)/(a-c)) YOUR ANSWER

This choice misuses the \(x\) values by calculating the change as \(a - c\) instead of \(c - a\). While the \(y\) change is correct, the incorrect \(x\) difference leads to an inaccurate representation of the slope.

Conclusion

To accurately determine the slope of a line between two points, the formula \(\frac{d-b}{c-a}\) must be used, where \(d\) and \(b\) are the \(y\) coordinates and \(c\) and \(a\) are the \(x\) coordinates of the points respectively. The other options contain errors in the arrangement of coordinates, leading to incorrect calculations of the slope. Understanding these distinctions is crucial for correctly analyzing linear relationships on graphs.

Two points (a,b) and (c,d) are shown on a graph. Which of the following equations correctly represents the slope of the line that passes through these points.

(d-b)/(c-a)

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test