Which pair of coordinates lie on the line with a slope of 2/3?
(1, 5) and (-2, 3)
(1, 5) and (8, 9)
(1, 5) and (-3, -2)
(1, 5) and (4, -6)
To determine if a pair of coordinates lies on a line with a slope of 2/3, we can use the slope formula.
The slope formula is given by:
m = (y2 - y1) / (x2 - x1)
Using the given coordinates:
For the pair (1, 5) and (-2, 3):
m = (3 - 5) / (-2 - 1)
= -2 / -3
= 2/3
The pair (1, 5) and (-2, 3) satisfies the equation, so it lies on the line with a slope of 2/3.
For the pair (1, 5) and (8, 9):
m = (9 - 5) / (8 - 1)
= 4 / 7
The pair (1, 5) and (8, 9) does not have a slope of 2/3.
For the pair (1, 5) and (-3, -2):
m = (-2 - 5) / (-3 - 1)
= -7 / -4
= 7/4
The pair (1, 5) and (-3, -2) does not have a slope of 2/3.
For the pair (1, 5) and (4, -6):
m = (-6 - 5) / (4 - 1)
= -11 / 3
The pair (1, 5) and (4, -6) does not have a slope of 2/3.
Therefore, the pair of coordinates (1, 5) and (-2, 3) lie on the line with a slope of 2/3.