The graph shows one of the linear equations for a system of equations. Which equation represents the second linear equation for the system of equations that has the solution which corresponds to a point at (6, -2)?
Responses
A
1/3x + 3y = 4
B
1/3x + 4y = −4
C
1/3x + 2y = −2
D
1/3x + 2y = 2
The equation that represents the second linear equation for the system of equations is C: 1/3x + 2y = -2.
u sure
I apologize for the confusion. Based on the given information, we are looking for the equation that represents the second linear equation for the system of equations that has the solution (6, -2).
To find the equation, we need to look for a line that passes through the point (6, -2) on the graph. Let's substitute the x and y values of the point (6, -2) into the equations given as options and see which one results in a true statement.
A) 1/3x + 3y = 4
Substituting x = 6 and y = -2:
1/3(6) + 3(-2) = 2 - 6 = -4
This is not true, so option A is not the correct answer.
B) 1/3x + 4y = −4
Substituting x = 6 and y = -2:
1/3(6) + 4(-2) = 2 - 8 = -6
This is not true, so option B is not the correct answer.
C) 1/3x + 2y = −2
Substituting x = 6 and y = -2:
1/3(6) + 2(-2) = 2 - 4 = -2
This is true, so option C is the correct answer.
D) 1/3x + 2y = 2
Substituting x = 6 and y = -2:
1/3(6) + 2(-2) = 2 - 4 = -2
This is true, so option D is also a valid answer. However, since option C is already confirmed as the correct answer, we do not need to consider option D.
Therefore, the equation that represents the second linear equation for the system of equations with the solution (6, -2) is C: 1/3x + 2y = -2.
Consider the following points:
M (-3, 4) N (-3, -4) O (0, -3) P (4, -3)
Which of the following is true of MP and NO ?
Responses
A They intersect at (3, -2).They intersect at (3, -2).
B They are parallel.They are parallel.
C They intersect at (-3, -4).They intersect at (-3, -4).
D They intersect at (0, -3).
To determine the relationship between MP and NO, we need to find their slopes.
MP: The coordinates of M are (-3, 4) and the coordinates of P are (4, -3). Using the slope formula, the slope of MP is (change in y)/(change in x):
m(MP) = (y2 - y1)/(x2 - x1) = (-3 - 4)/(4 - (-3)) = -7/7 = -1.
NO: The coordinates of N are (-3, -4) and the coordinates of O are (0, -3). Using the slope formula, the slope of NO is:
m(NO) = (y2 - y1)/(x2 - x1) = (-3 - (-4))/(0 - (-3)) = 1/3.
Comparing the slopes, we can see that the slopes of MP and NO are not the same. Therefore, MP and NO are not parallel.
To find out where MP and NO intersect, we can set the equations of the lines equal to each other:
-1 = 1/3.
This equation is not true, so MP and NO do not intersect at any point.
Therefore, the correct answer is B: MP and NO are parallel.
are you sure you have the right answer.
I apologize for the incorrect response. Let's reassess the situation.
MP: The coordinates of M are (-3, 4) and the coordinates of P are (4, -3). We can calculate the slope of MP using the slope formula:
m(MP) = (y2 - y1)/(x2 - x1) = (-3 - 4)/(4 - (-3)) = (-7)/(7) = -1.
NO: The coordinates of N are (-3, -4) and the coordinates of O are (0, -3). The slope of NO can be calculated as:
m(NO) = (y2 - y1)/(x2 - x1) = (-3 - (-4))/(0 - (-3)) = 1/3.
The slopes of MP and NO are not equal, so they are not parallel.
To determine if MP and NO intersect, we can compare the x and y values of the points M, N, P, and O. From the given points:
M (-3, 4)
N (-3, -4)
O (0, -3)
P (4, -3)
We can see that the x-coordinate of P is 4 and the x-coordinate of N is -3. Since the x-coordinates are different and the slopes are not equal, MP and NO will intersect at some point.
Therefore, the correct answer is: D) They intersect at (0, -3).