#2.
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 equations is represented by both lines?
x
-10
-4
2
10
y
8
5
2
-2
answer choices:
y=-1/3x-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, we need to find the equation of the second line using the provided points in the table.
Looking at the table, we can see that the x-values are increasing by 6 each time (from -10 to -4 to 2 to 10), and the y-values are decreasing by 3 each time (from 8 to 5 to 2 to -2).
We can use the point-slope formula to find the equation of the second line. Choosing the point (2, 2) from the table, we have:
y - y1 = m(x - x1)
y - 2 = -(3/3)(x - 2)
y - 2 = -(1/3)(x - 2)
Multiplying through by 3:
3y - 6 = -x + 2
3y = -x + 8
y = (-1/3)x + 8/3
Therefore, the second line is represented by the equation y = (-1/3)x + 8/3.
Comparing this equation with the answer choices, we can see that the correct answer is A y = (-1/3)x - 3 and y = (1/2)x + 2.