Question

The table of ordered pairs represent some points on the graphs of lines q and v.

Line q Line v
x
−9
−3
2
y
0
18
33

x
−4
0
10
y
10
8
3


Which system of equations is represented by lines q and v?
A.
21x−y=9
5x+6y=40

B.
3x−y=−27
x+2y=16

C.
21x−y=9
5x+6y=20

D.
9x−y=−27
x+2y=8

Answer 1

To determine the system of equations represented by lines q and v, we need to analyze the ordered pairs for both lines and derive equations from them.

For Line q:
- The points are (-9, 0), (-3, 18), and (2, 33).
- We can find the slope (m) using two points:

Using points (-9, 0) and (-3, 18):
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{18 - 0}{-3 - (-9)} = \frac{18}{6} = 3
\]

Now, using the slope and one of the points to form the line's equation:
Using point (-9, 0):
\[
y - 0 = 3(x + 9) \\
y = 3x + 27
\]

Rearranging to standard form:
\[
3x - y = -27
\]

So, the equation for Line q is:
\[
3x - y = -27
\]

For Line v:
- The points are (-4, 10), (0, 8), and (10, 3).
- Again, we can calculate the slope using two points:

Using points (-4, 10) and (0, 8):
\[
m = \frac{8 - 10}{0 - (-4)} = \frac{-2}{4} = -\frac{1}{2}
\]

Now, using the slope and point (0, 8) to form the line's equation:
\[
y - 8 = -\frac{1}{2}(x - 0) \\
y = -\frac{1}{2}x + 8
\]

Rearranging to standard form:
\[
x + 2y = 16
\]

So, the equation for Line v is:
\[
x + 2y = 16
\]

Thus, the system of equations represented by lines q and v is:
\[
3x - y = -27 \\
x + 2y = 16
\]

Looking at the options provided:
B.
3x−y=−27
x+2y=16

This matches our derived equations.

Therefore, the correct answer is:
**B. 3x−y=−27 and x+2y=16**.