A system of linear equations is represented by line j and a table of values. The graph of line j is shown at the left and the points of another line are shown in the table. Which system of equation is represented by both lines?
X
-10
-4
2
10
Y
8
5
2
-2
A. Y=-2/3x-3
Y=1/2x+2
B. Y=2/3x+2
Y=-1/2x+3
C. Y=3/2x+2
Y=-2x-3
D. Y=3x+2
Y=-2x+3
To determine which system of equations is represented by both lines given the points in the table, we need to find the equation of the line represented by the points in the table.
We can first find the slope of the line represented by the points (-10, 8) and (10, -2).
m = (y2 - y1) / (x2 - x1)
m = (-2 - 8) / (10 - (-10))
m = (-10) / 20
m = -1/2
Next, we can choose one of the points to find the equation of the line using the point-slope form of the equation of a line:
y - y1 = m(x - x1)
Choosing the point (-10, 8):
y - 8 = -1/2(x - (-10))
y - 8 = -1/2(x + 10)
y - 8 = -1/2x - 5
y = -1/2x + 3
Therefore, the system of equations represented by both lines is:
Y = -1/2x + 3