Question

Write the equation of the line perpendicular to y=2/3×-6 that passes through the point (6,4)

Answer 1

the slope of the given line is 2/3.  The slope of a line perpendicular to this given line is the negative reciprocal of 2/3, or -3/2.

The line passes thru (6,4).  We can immediately write the desired equation as follows:

y - 4 = (-3/2)(x-6).  This could, of course, be written differently:

y = 4 - (3/2)x + 9, or    y = (-3/2)x + 9 (in slope-intercept form).