1 answer
(click or scroll down)
Bot GPT 3.5 To determine which two points the line could pass through, we need to find the equation of the line using the given slope and then check if the equation is satisfied by any of the given point pairs.
The equation of a line can be written in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
Given that the slope is -5/3, the equation of the line is y = (-5/3)x + b.
To find the y-intercept b, we can substitute the x and y values of one of the given points into the equation. Let's choose point (12,13):
13 = (-5/3)(12) + b
13 = -20 + b
b = 33
So, the equation of the line is y = (-5/3)x + 33.
Now, let's check if any of the other given point pairs satisfy this equation:
A. (12,13),(17,10):
For point (12,13): 13 = (-5/3)(12) + 33
13 = -20 + 33
13 = 13 (satisfied)
For point (17,10): 10 = (-5/3)(17) + 33
10 = -85/3 + 99/3
10 = 14/3 (not satisfied)
B. (16,15),(13,10):
For point (16,15): 15 = (-5/3)(16) + 33
15 = -80/3 + 99/3
15 = 19/3 (not satisfied)
For point (13,10): 10 = (-5/3)(13) + 33
10 = -65/3 + 99/3
10 = 34/3 (not satisfied)
C. (0,7),(3,10):
For point (0,7): 7 = (-5/3)(0) + 33
7 = 33 (not satisfied)
For point (3,10): 10 = (-5/3)(3) + 33
10 = -15/3 + 99/3
10 = 28/3 (not satisfied)
D. (11,13),(8,18):
For point (11,13): 13 = (-5/3)(11) + 33
13 = -55/3 + 99/3
13 = 44/3 (not satisfied)
For point (8,18): 18 = (-5/3)(8) + 33
18 = -40/3 + 99/3
18 = 59/3 (not satisfied)
The only point pair that satisfies the equation of the line is A. (12,13),(17,10). Therefore, the line could pass through points (12,13) and (17,10).