which of the following pairs of points both lie on the line whose equation is 3x-y=2?
a)(2,-2) and (1,5)
b)(2,4) and (1,5)
c)(2,4) and (3,7)
d)(3,7) and (3,-2)
C. (2,4) and (3,7)
To determine which pair of points lie on the line whose equation is 3x - y = 2, we can substitute the x and y values of each pair into the equation and check if the equation holds true.
a) (2,-2):
Substituting these values into the equation:
3(2) - (-2) = 2
6 + 2 = 2
8 = 2
This equation is not true, so the pair (2,-2) does not lie on the line.
b) (2,4):
Substituting these values into the equation:
3(2) - 4 = 2
6 - 4 = 2
2 = 2
This equation is true, so the pair (2,4) lies on the line.
c) (2,4):
Substituting these values into the equation:
3(2) - 4 = 2
6 - 4 = 2
2 = 2
This equation is true, so the pair (2,4) lies on the line.
d) (3,7):
Substituting these values into the equation:
3(3) - 7 = 2
9 - 7 = 2
2 = 2
This equation is true, so the pair (3,7) lies on the line.
d) (3,7):
Substituting these values into the equation:
3(3) - (-2) = 2
9 + 2 = 2
11 = 2
This equation is not true, so the pair (3,-2) does not lie on the line.
So, the pairs of points that both lie on the line whose equation is 3x - y = 2 are:
b) (2,4) and (1,5)
c) (2,4) and (3,7)
To determine which pairs of points lie on the line with the equation 3x - y = 2, we need to substitute the x and y values of each pair of points into the equation and see if it holds true.
Let's check each option:
a) For pair (2, -2):
3(2) - (-2) = 6 + 2 = 8
The equation 3x - y = 2 does not hold true for this pair of points.
For pair (1, 5):
3(1) - 5 = 3 - 5 = -2
The equation 3x - y = 2 does not hold true for this pair of points.
Since neither of the points in option a) satisfies the equation, we can eliminate this option.
b) For pair (2, 4):
3(2) - 4 = 6 - 4 = 2
The equation 3x - y = 2 holds true for this pair of points.
For pair (1, 5):
3(1) - 5 = 3 - 5 = -2
The equation 3x - y = 2 does not hold true for this pair of points.
Therefore, option b) is valid since one of the points satisfies the equation.
c) For pair (2, 4):
3(2) - 4 = 6 - 4 = 2
The equation 3x - y = 2 holds true for this pair of points.
For pair (3, 7):
3(3) - 7 = 9 - 7 = 2
The equation 3x - y = 2 also holds true for this pair of points.
Therefore, option c) is valid since both points satisfy the equation.
d) For pair (3, 7):
3(3) - 7 = 9 - 7 = 2
The equation 3x - y = 2 holds true for this pair of points.
For pair (3, -2):
3(3) - (-2) = 9 + 2 = 11
The equation 3x - y = 2 does not hold true for this pair of points.
Therefore, option d) is also valid since one of the points satisfies the equation.
In conclusion, the pairs of points that both lie on the line with the equation 3x - y = 2 are:
b) (2, 4) and (1, 5)
c) (2, 4) and (3, 7)
d) (3, 7) and (3, -2)