The tables of ordered pairs represent some points on the graphs of two different lines.

Question

Which system of equations represents the graph of these two lines?

Question 1 options:

x - 6y = -90
x - 3y = 27

x + 6y = 90
x + 3y = -27

6x - y = -15
3x - y = 9

6x + y = 15
3x + y = -9

Answer 1

To determine which system of equations represents the graphs of the two lines based on the ordered pairs you have, we first need to extract the ordered pairs' values, which might look like (x1, y1), (x2, y2), etc. Unfortunately, those points are not provided here.

However, here's a general way to find the correct system of equations:

1. Identify Points: Determine several ordered pairs from the points given.

2. Substitute Points into Equations: For each option provided, substitute the x and y values of the ordered pairs into each equation. If the pairs satisfy the equations, that equation represents a line passing through the points.

3. Determine Slope and Intercept (if necessary): For clarity, you might convert each equation into slope-intercept form (y = mx + b) to better understand the relationship.

Since the actual points are missing, follow these steps using the points if you have them to determine which system matches.

If you provide the ordered pairs, I can help you more specifically to solve the problem.

Answer 2

line a
x= -11 , -6, -1, 4
y= 81, 51, 21, -9

Line b
x= -9, -4, 1, 6
y= 18, 3, -12, -27

Answer 3

Thank you for providing the ordered pairs for the two lines. Let's identify the equations that represent each line based on the given points.

Line A Points:

• (-11, 81)
• (-6, 51)
• (-1, 21)
• (4, -9)

Line B Points:

• (-9, 18)
• (-4, 3)
• (1, -12)
• (6, -27)

Now, we'll first find the equations of both lines by calculating their slopes and y-intercepts.

Finding the Equation of Line A:

1. Calculate the Slope (m): Using points (-11, 81) and (4, -9):

   \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-9 - 81}{4 - (-11)} = \frac{-90}{15} = -6 \]

2. Use Point-Slope Form: \[ y - y_1 = m(x - x_1) \] Using point (-11, 81):

   \[ y - 81 = -6(x + 11) \] \[ y - 81 = -6x - 66 \] \[ y = -6x + 15 \]

   Re-arranging gives: \[ 6x + y = 15 \]

Finding the Equation of Line B:

1. Calculate the Slope (m): Using points (-9, 18) and (6, -27):

   \[ m = \frac{-27 - 18}{6 - (-9)} = \frac{-45}{15} = -3 \]

2. Use Point-Slope Form: Using point (-9, 18):

   \[ y - 18 = -3(x + 9) \] \[ y - 18 = -3x - 27 \] \[ y = -3x - 9 \]

   Re-arranging gives: \[ 3x + y = -9 \]

Summary of Equations:

• Line A: \(6x + y = 15\)
• Line B: \(3x + y = -9\)

Matching with Options:

Now, let's compare the resulting equations with the provided options:

1. \(6x + y = 15\) (Matches with option \(6x + y = 15\))
2. \(3x + y = -9\) (Matches with option \(3x + y = -9\))

Therefore, the correct system of equations that represents the graphs of these two lines is:

Option: \(6x + y = 15\) and \(3x + y = -9\).