A line has slope negative five-thirds. Through which two points could this line pass?
(1 point)
Responses
(12, 13) and (17, 10)
(16, 15) and (13, 10)
(0, 7) and (3, 10)
(11, 13) and (8, 18)
To find the line that has a slope of negative five-thirds and passes through two points, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Where m is the slope and (x1, y1) are the coordinates of a point on the line.
Let's check which pair of points satisfies the equation:
For (12, 13) and (17, 10):
Using the point-slope form with the first point (12, 13):
y - 13 = (-5/3)(x - 12)
Multiplying through by 3:
3y - 39 = -5(x - 12)
3y - 39 = -5x + 60
3y = -5x + 99
Substituting the x-coordinate of the second point (17, 10):
3(10) = -5(17) + 99
30 = -85 + 99
30 = 30
This pair of points satisfies the equation.
For (16, 15) and (13, 10):
Using the point-slope form with the first point (16, 15):
y - 15 = (-5/3)(x - 16)
Multiplying through by 3:
3y - 45 = -5(x - 16)
3y - 45 = -5x + 80
3y = -5x + 125
Substituting the x-coordinate of the second point (13, 10):
3(10) = -5(13) + 125
30 = -65 + 125
30 = 60
This pair of points does not satisfy the equation.
For (0, 7) and (3, 10):
Using the point-slope form with the first point (0, 7):
y - 7 = (-5/3)(x - 0)
Multiplying through by 3:
3y - 21 = -5x
3y = -5x + 21
Substituting the x-coordinate of the second point (3, 10):
3(10) = -5(3) + 21
30 = -15 + 21
30 = 6
This pair of points does not satisfy the equation.
For (11, 13) and (8, 18):
Using the point-slope form with the first point (11, 13):
y - 13 = (-5/3)(x - 11)
Multiplying through by 3:
3y - 39 = -5(x - 11)
3y - 39 = -5x + 55
3y = -5x + 94
Substituting the x-coordinate of the second point (8, 18):
3(18) = -5(8) + 94
54 = -40 + 94
54 = 54
This pair of points satisfies the equation.
Thus, the line with a slope of negative five-thirds could pass through the points (12, 13) and (17, 10) or (11, 13) and (8, 18).