What is an equation of the line that is perpendicular to y= −3/4x +6 and passes through the point (3, 9) ?

Perpendicular lines have opposite reciprocals from the original line.

Original line: y=-3/4x+6

Perpendicular line: y=4/3x+b

Solve for b by plugging in the given coordinates (3,9) for x and y respectively.

9=4/3(3)+b

Multiply 4/3*3.

9=4+b

Subtract 4 from both sides.

5=b

Now, with b and the slope, you can write the equation:

y=4/3x+5

I hope this helps :)