Final answer:
The equation of the line is y = 4/3x - 7.
Step-by-step explanation:
The equation in slope-intercept form of a line is given by y = mx + b, where m represents the slope and b represents the y-intercept.
To find the equation of a line perpendicular to another line, we need to determine the negative reciprocal of the slope of the given line. In this case, the slope of the given line is -3/4, so the negative reciprocal is 4/3.
Since the line passes through the point (12, 9), we can substitute these values into the equation to solve for b. Using the equation y = mx + b and substituting m = 4/3, x = 12, and y = 9, we get:
9 = (4/3)(12) + b
Solving for b gives:
b = 9 - (4/3)(12)
Simplifying further, we get:
b = 9 - 16
b = -7
Therefore, the equation of the line that passes through (12, 9) and is perpendicular to the graph of y = -3/4x + 1 is y = 4/3x - 7.