The correct graph is A.
The first equation is y = -3/4x + 2. This can be rewritten as y - 2 = -3/4x. Solving for x, we get x = (4/3)(y - 2).
The second equation is y = -1/2x - 1. This can be rewritten as y + 1 = -1/2x. Solving for x, we get x = -2(y + 1).
The two lines intersect at the point (0, 2). Plugging in x = 0 into both equations, we get y = 2 for both equations. Therefore, the two lines must intersect at the point (0, 2).
The slope of the first line is -3/4. The slope of the second line is -1/2. The slopes are negative inverses of each other. Therefore, the two lines are perpendicular.
A coordinate grid with one line that passes through the points 0 comma 2 and 4 comma negative 1 and another line that passes through the points 0 comma negative 1 and 1 comma negative 3 is incorrect because the two lines are not perpendicular.
A coordinate grid with one line that passes through the points 0 comma 2 and 3 comma negative 2 and another line that passes through the points 0 comma negative 1 and negative 1 comma 1 is incorrect because the two lines intersect at the point (0, 2).
A coordinate grid with one line that passes through the points 0 comma 2 and 3 comma negative 2 and another line that passes through the points 0 comma negative 1 and 2 comma negative 2 is incorrect because the two lines are not perpendicular.