The correct equations for the system shown on the graph are y = -1/4x -2/5 and y = 2x - 4.
To determine which equations are represented by the graph, we can first identify the slopes and y-intercepts of the two lines. The slope of the first line is -1/4 and its y-intercept is -2/5. The slope of the second line is 2 and its y-intercept is -4.
We can then use the point-slope form of linear equations to write down the equations for each line. The point-slope form is:
y - y_1 = m(x - x_1)
where m is the slope of the line and (x_1, y_1) is a point on the line.
For the first line, we can use the point (0, -2/5) to write down the equation
y - (-2/5) = -1/4(x - 0)
This simplifies to:
y = -1/4x - 2/5
For the second line, we can use the point (-2, -4) to write down the equation:
y - (-4) = 2(x - (-2))
This simplifies to:
y = 2x - 4
Therefore, the correct equations for the system shown on the graph are y = -1/4x - 2/5 and y = 2x - 4.