Final answer:
The equation of the line that is perpendicular to y = -3/4 x + 1 and passes through the point (12, 9) is y = 4/3x - 7.
Step-by-step explanation:
A student has asked for the equation of a line that is perpendicular to the line represented by y = -3/4 x + 1 and passes through the point (12, 9). To find the equation of a perpendicular line, first, we need to determine the slope of the original line, which is -3/4. The slope of a line perpendicular to this would be the negative reciprocal, so in this case, the slope of the perpendicular line would be 4/3. With the slope and a given point, we can use the point-slope form of a line to find its equation. The point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through.
Substituting the given slope and point into the point-slope form yields:
y - 9 = 4/3(x - 12)
Simplifying, we first distribute the slope across the right side:
y - 9 = 4/3x - 16
Then we add 9 to both sides to solve for y:
y = 4/3x - 7
This is the equation of the line that is perpendicular to y = -3/4 x + 1 and passes through the point (12, 9).