Write the equation of the line perpendicular to the given line and passing through the given point: y=3x−2 through (3,4)

The equation of the given line, y = 3x - 2, is written in slope-intercept form:

... y = mx + b

where m represents the slope and b is the y-intercept.

Matching the form to the given equation, you see m = 3, and b = -2. The slope of the given line is 3.

The slope of a line perpendicular to it will be the negative reciprocal of this value

... slope of perpendicular line = -1/m = -1/3

For some new value of b, the equation of the perpendicular line can be written

... y = (-1/3)x + b

Filling in the values of the point coordinates, we can find the appropriate value of b.

... 4 = (-1/3)(3) +b

... 4 = -1 + b . . . . . . . simplify

... 5 = b . . . . . . . . . . add 1

Then the equation you want is ...

... y = (-1/3)x + 5