find an equation of the line that passes through (3,4) and is perpendicular to y=3x-6

Question

find an equation of the line that passes through (3,4) and is perpendicular to y=3x-6

Answer 1

The line defined by the equation  y=3x-6  has a slope of 3.  All lines perpendicular to it have a slope of -1/3 (the negative reciprocal of 3).

 

So far, the equation of the perpendicular line in slope-intercept form is y = (-1/3)x + b and we can use the point (3,4) to determine b.

      4 = (-1/3)(3) + b

      4 = -1 + b

      5 = b

 

The equation of the perpendicular line is:   y= (-1/3)x + 5

Answer 2

The line perpendicular to y = 3x - 6 must have a slope, the negative reciprocal of 3.  Thus, the slope of the new line is -1/3. Since the new line passes through the poin (3, 4), we can substitute the values into the general eqution of a line.  Thus, we have 4 = 3(3) + b.  Solving for b, we get b= -5.  Therefore, the new equation is y =(-1/3)x - 5.