A line has a slope of 3/5. Through which two points could this line pass?
Responses
a. (8, 1) and (5, 0)
b. (6, 3) and (11, 6)
c. (-9, 7) and (4, -3)
d. (-7, -2) and (5, 21)
To determine if a line can pass through two given points, we can calculate the slope between those two points and see if it matches the given slope of 3/5.
Let's calculate the slope between the first pair of points (8, 1) and (5, 0):
slope = (y2 - y1)/(x2 - x1)
= (0 - 1)/(5 - 8)
= -1/-3
= 1/3
The calculated slope of 1/3 does not match the given slope of 3/5. Therefore, the line does not pass through these points.
Now, let's calculate the slope between the second pair of points (6, 3) and (11, 6):
slope = (6 - 3)/(11 - 6)
= 3/5
The calculated slope of 3/5 matches the given slope of 3/5. Therefore, the line can pass through these points.
Next, let's calculate the slope between the third pair of points (-9, 7) and (4, -3):
slope = (-3 - 7)/(4 - (-9))
= -10/13
The calculated slope of -10/13 does not match the given slope of 3/5. Therefore, the line does not pass through these points.
Finally, let's calculate the slope between the fourth pair of points (-7, -2) and (5, 21):
slope = (21 - (-2))/(5 - (-7))
= 23/12
The calculated slope of 23/12 does not match the given slope of 3/5. Therefore, the line does not pass through these points.
In conclusion, the line with a slope of 3/5 can only pass through the second pair of points (6, 3) and (11, 6). Answer: b. (6, 3) and (11, 6).