The tables of ordered pairs represent some points on the graphs of lines q and v.
Line q
X: -9, -3, 2
Y: 0, 18, 33
Line v
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
To determine which system of equations is represented by lines q and v, we first need to find the equations of the lines using the given points.
For Line q:
Using the points (-9, 0) and (-3, 18), we can find the slope: (18 - 0) / (-3 - (-9)) = 18 / 6 = 3.
Using the point-slope equation, we get the equation of Line q as y = 3x + 27.
For Line v:
Using the points (-4, 10) and (0, 8), we can find the slope: (8 - 10) / (0 - (-4)) = -2 / 4 = -1/2.
Using the point-slope equation, we get the equation of Line v as y = -1/2x + 8.
Comparing these equations with the options:
A. 21x - y = 9, 5x + 6y = 40
Both equations do not match the equations of Line q and Line v.
B. 3x - y = -27, x + 2y = 16
Both equations do not match the equations of Line q and Line v.
C. 21x - y = 9, 5x + 6y = 20
The first equation does not match the equation of Line q. The second equation partially matches the equation of Line q, but the constants do not match Line v.
D. 9x - y = -27, x + 2y = 8
The first equation does not match the equation of Line q. The second equation matches the equation of Line v.
Therefore, the system of equations represented by lines q and v is D. 9x - y = -27, x + 2y = 8.