Write a slope intercept form the equation of a line that goes through (-3,4) and is perpendicular to the following y=3x-2

Slope intercept form : y=mx+b ; where m=slope, b=y-intercept

Passes through (-3, 4) and is perpendicular to the line : y = 3x - 2

**Remember : if a line is perpendicular to something, then you simply take the slope's negative reciprocal**

Slope 1 = 3 (as 3 is in the "m" spot, which is slope). 
Slope 2 = -1/3 (because it is the negative reciprocal)

So, plug in the new slope into slope intercept form

y = mx + b → y = -1/3x + b

Remember that it passes through (-3, 4) so we use that to help us find "b" which is our y-intercept.

Plug in -3 for x, and 4 for y

y = mx+b

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

Simplify.

4= 1 + b

Subtract 1 from both sides.

3 = b → Therefore, b = 3:)

So now we simply plug everything in !!

**Remember : slope = -1/3, b = 3**

y = mx + b

y = -1/3x + 3

~hope I helped!~