To determine which system of equations represents the graph of the two given lines, we can first find the equations of the lines using the points provided.
For Line a:
Using the points (-11, 81) and (4, -9), we can calculate the slope:
m = (y2 - y1) / (x2 - x1)
m = (-9 - 81) / (4 - (-11))
m = -90 / 15
m = -6
The equation of Line a using the point (-11, 81) can be found using the point-slope formula:
y - y1 = m(x - x1)
y - 81 = -6(x + 11)
y - 81 = -6x - 66
y = -6x + 15 (Equation 1)
For Line b:
Using the points (-9, 18) and (6, -27), we can calculate the slope:
m = (y2 - y1) / (x2 - x1)
m = (-27 - 18) / (6 - (-9))
m = -45 / 15
m = -3
The equation of Line b using the point (-9, 18) can be found using the point-slope formula:
y - y1 = m(x - x1)
y - 18 = -3(x + 9)
y - 18 = -3x - 27
y = -3x - 9 (Equation 2)
Now, compare the two equations with the answer choices:
A) x - 6y = -90, x - 3y = 27
Substitute for x and y using Line a equation:
-6(-6x + 15) = -90
36x - 90 = -90
36x = 0
x = 0 (not true)
Substitute for x and y using Line b equation:
-3(-3x - 9) = 27
9x + 27 = 27
9x = 0
x = 0 (not true)
B) x + 6y = 90, x + 3y = -27
Substitute for x and y using Line a equation:
-6 + 15 = 90
9 = 90 (not true)
Substitute for x and y using Line b equation:
-3 - 9 = -27
-12 = -27 (not true)
C) 6x - y = -15, 3x - y = -9
Substitute for x and y using Line a equation:
6(-6) - 21 = -15
-36 - 21 = -15
-57 = -15 (not true)
Substitute for x and y using Line b equation:
3(-3) - 21 = -9
-9 - 18 = -9
-27 = -9 (not true)
D) 6x + y = 15, 3x + y = -9
Substitute for x and y using Line a equation:
6(-6) + 15 = 15
-36 + 15 = 15
-21 = 15 (not true)
Substitute for x and y using Line b equation:
3(-3) + 21 = -9
-9 + 18 = -9
9 = -9 (not true)
None of the answer choices accurately represent the system of equations for the given lines.
the tables of ordered pairs represent some points on the graphs of two different lines.
Line a
X: -11, -6, -1, 4
Y: 81, 51, 21, -9
Line b
X: -9, -4, 1, 6
Y: 18, 3, -12, -27
Which systems of equations represents the graph of these two lines?
A) x - 6y = -90, x - 3y = 27
B) x + 6y = 90, x + 3y = -27
C) 6x - y = -15, 3x - y = -9
D) 6x + y = 15, 3x + y = -9
1 answer