The line passes through (-6,9)
perpendicular to y=3x-2

The key to understand this problem is that perpendicular lines have slopes that are the negative reciprocals of each other. Example, a line with slope 3/4 has a perpendicular with a slope of -4/3. So flip it over and take the negative. Like 7/12 and -12/7 or 2 and -1/2 (because 2 = 2/1)

The slope of y = 3x - 2 is 3 (the number preceding the "x' if the line is in the form y = mx + b)

So the line perpendicular to y = 3x - 2 has a slope of -1/3.

So now you just need to write the equation of the line with slope -1/3 that goes through (-9, 5). Use the point-slope form, y - y1 = m(x - x1) where (x1, y1) is (-9, 5) and m = -1/3

y - 5 = -1/3(x - -9)

y - 5 = -1/3(x + 9)

That's the answer. If they want you to give the answer in the y= mx + b format (slope-intercept) then multiply it out and combine like terms.

y - 5 = -1/3(x + 9)

y - 5 = -1/3x - 3

y = -1/3x + 2

3

step-by-step explanation: