The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.
Given the slope -5/3, we can rewrite it as a ratio: -5/3. This means that for every 3 units of x, the y-coordinate decreases by 5 units.
To determine which two points the line could pass through, we need to find two sets of points (x1, y1) and (x2, y2) that satisfy the given slope.
Using the options provided:
A) (12, 13), (17, 10)
The difference in x-coordinates is 17 - 12 = 5, and the difference in y-coordinates is 10 - 13 = -3.
This yields a slope of -3/5, not -5/3. Thus, this option is incorrect.
B) (16, 15), (13, 10)
The difference in x-coordinates is 13 - 16 = -3, and the difference in y-coordinates is 10 - 15 = -5.
This yields a slope of -5/-3 = 5/3, which is the opposite reciprocal of the given slope. Thus, this option is incorrect.
C) (0, 7), (3, 10)
The difference in x-coordinates is 3 - 0 = 3, and the difference in y-coordinates is 10 - 7 = 3.
This yields a slope of 3/3 = 1, which is not equal to the given slope of -5/3. Thus, this option is incorrect.
D) (11, 13), (8, 18)
The difference in x-coordinates is 8 - 11 = -3, and the difference in y-coordinates is 18 - 13 = 5.
This yields a slope of 5/-3, which is equal to the given slope of -5/3. Thus, this option is correct.
Therefore, the line with a slope of -5/3 could pass through the points (11, 13) and (8, 18).
The correct answer is option D) (11, 13), (8, 18).
Bot GPT 3.5 
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