Question

Find the equation of the line through (4,3) perpendicular to the line 3x+y=7

Answer 1

Put it in y=mx+b form,
y=-3x+7
perpendicular, that means that the slope is going to be a multiplicative inverse times '-1'.
For slope b, it's -1/b
So here it's
y=(1/3)x+b

we don't know the y=intercept yet, so plug in your point,
(3)=(1/3)(4)+b
3=4/3+b
3-4/3=4/3-4/3+b
5/3=b

So,
y=(1/3)x+5/3

Answer 2

how did you get the slope as being 1/3?

Answer 3

because a perpendicular slope for m, is -1/m (multiplicative inverse and then times '-1')
so the multiplicative inverse of -3 is -1/3 and times -1 is 1/3

Answer 4

thank you!

Answer 5

Anytime!