7. 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.
Answer: B
The equation that correctly represents the slope of the line through the points (a,b) and (c,d) is (d-b)/(c-a).
The slope of a line passing through two points (a,b) and (c,d) is calculated as the change in y divided by the change in x. Therefore, the correct formula is (d-b)/(c-a).
A) (b-d)/(a-c
This option incorrectly calculates the slope by reversing the order of the points. The slope should be determined by the change in y values from d to b, resulting in (d-b), and the change in x values should be from a to c, leading to (c-a). Thus, this option is incorrect.
B) (d-b)/(c-a)
This option correctly represents the slope of the line connecting the points (a,b) and (c,d). It accurately calculates the change in y values (d-b) and the change in x values (c-a), following the standard slope formula.
C) (b-d)/(c-a)
This option incorrectly reverses the order of the y values, calculating the slope as (b-d) instead of (d-b). The correct representation of the slope must reflect the change from d to b, making this option incorrect.
D) (d-b)/(a-c)
This option incorrectly uses (a-c) for the change in x values. The correct denominator should be (c-a), as the change is between the x-coordinates a and c. Therefore, this option is also incorrect.
Conclusion
The correct formula for the slope is (d-b)/(c-a), as it accurately represents the vertical change in y divided by the horizontal change in x. All other options miscalculate either the order of the y values or the x values, leading to incorrect representations of the slope.