Final answer:
The equation of a line perpendicular to y=3/4x is y = -4/3x + 10/3.
Step-by-step explanation:
The equation of a line perpendicular to y = 3/4x will have a slope that is the negative reciprocal of the original line's slope. The original slope is 3/4, so the perpendicular line's slope will be -4/3.
Using the point-slope form of a linear equation, we can choose any point on the line and plug it into the equation: y - y1 = m(x - x1). Let's say we choose the point (1, 2):
y - 2 = -4/3(x - 1)
Simplifying the equation gives us: y = -4/3x + 10/3. Therefore, the equation of a line perpendicular to y = 3/4x is y = -4/3x + 10/3.