A line has slope –. Through which two points could this line pass?
A.(12, 13), (17, 10)
B.(16, 15), (13, 10)
C.(0, 7), (3, 10)
D.(11, 13), (8, 18)
I think it is A?
i think D
To determine which two points the line could pass through given a slope, we can use the slope-intercept form of a linear equation: y = mx + b, where m represents the slope and b represents the y-intercept.
In this case, the given slope is -1/2.
To find the equation of the line using the slope-intercept form, we need to determine the value of b. Since we do not have the y-intercept, we can use either of the two points to find it.
Let's choose option A: (12, 13) and (17, 10).
First, calculate the slope using these two points:
m = (y₂ - y₁) / (x₂ - x₁)
m = (10 - 13) / (17 - 12)
m = -3 / 5
Comparing the calculated slope (-3/5) with the given slope (-1/2), we see that they do not match. Therefore, option A is incorrect.
Now, let's try the second option: (16, 15) and (13, 10).
Calculate the slope using these two points:
m = (10 - 15) / (13 - 16)
m = -5 / -3
m = 5/3
Again, the calculated slope (5/3) does not match the given slope (-1/2). Therefore, option B is also incorrect.
Moving on to the third option: (0, 7) and (3, 10).
Calculate the slope using these two points:
m = (10 - 7) / (3 - 0)
m = 3 / 3
m = 1
The calculated slope (1) matches the given slope (-1/2). Therefore, option C is the correct answer.
Finally, let's verify option D using the same process.
For option D: (11, 13) and (8, 18).
Calculate the slope using these two points:
m = (18 - 13) / (8 - 11)
m = 5 / -3
Once again, the calculated slope (5/-3) does not match the given slope (-1/2). Therefore, option D is incorrect.
In conclusion, the line with a slope of -1/2 could pass through points (0, 7) and (3, 10), which corresponds to option C.