To determine which of the given points lie on the graph of the equation y = 9|x|, substitute the x and y-values of each point into the equation and see if the equation holds true.
1) For the point (-5, 45):
When x = -5,
y = 9|-5| = 9(5) = 45
Since y = 45, this point is on the graph of the equation.
2) For the point (5, 45):
When x = 5,
y = 9|5| = 9(5) = 45
Since y = 45, this point is on the graph of the equation.
3) For the point (-(1/4), -(9/4)):
When x = -(1/4),
y = 9|-(1/4)| = 9(1/4) = 9/4
Since y = -(9/4), this point is not on the graph of the equation.
Therefore, the points (-5, 45) and (5, 45) lie on the graph of the equation y = 9|x|.