A line has slope-5/3. 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)
To determine the equation of a line given its slope and two points, we can use the point-slope form: y - y₁ = m(x - x₁), where m is the slope of the line, and (x₁, y₁) are the coordinates of a point on the line.
Let's calculate the equation using option A: (12,13),(17,10)
The slope of the line is -5/3. Let's choose the point (12,13), which gives us:
y - 13 = (-5/3)(x - 12)
y - 13 = (-5/3)x + 20
y = (-5/3)x + 33
If we substitute the coordinates of the other point (17,10) into the equation, we can verify if it satisfies the equation:
10 = (-5/3)(17) + 33
10 = -85/3 + 99/3
10 = 14/3
This equation is not satisfied, so option A is not correct.
Let's check option B: (16,15),(13,10)
Using the same process, we find the equation to be:
y - 15 = (-5/3)(x - 16)
y - 15 = (-5/3)x + 80/3
y = (-5/3)x + 125/3
Substituting the coordinates of the second point:
10 = (-5/3)(13) + 125/3
10 = -65/3 + 125/3
10 = 60/3
10 = 20/3
This equation is not satisfied, so option B is not correct.
Let's check option C: (0,7), (3,10)
Proceeding with the same steps, we get:
y - 7 = (-5/3)(x - 0)
y - 7 = (-5/3)x
y = (-5/3)x + 7
Substituting the values from the second point equation:
10 = (-5/3)(3) + 7
10 = -15/3 + 21/3
10 = 6/3
10 = 2
This equation is not satisfied, so option C is not correct.
Finally, let's check option D: (11,13), (8,18)
Following the same steps as before, we find the equation to be:
y - 13 = (-5/3)(x - 11)
y - 13 = (-5/3)x + 55/3
y = (-5/3)x + 94/3
Now substituting the coordinates of the second point:
18 = (-5/3)(8) + 94/3
18 = -40/3 + 94/3
18 = 54/3
18 = 18
This equation is satisfied, so option D is correct.
Therefore, the line with a slope of -5/3 could pass through points (11,13) and (8,18), making option D the correct answer.