Question

I need to find an equation of the line that passes through (3,4) and is perpendicular to y = 3x-7. What is the equation of the line? how did you get the answer? this is algebra.

Answer 1

Perpendicular lines have exact opposite slopes so if your first line has 3x then your perpendicular slope would be -1/3x, your y-intercept needs to be on the same path as (3,4). When in doubt graph.

Answer 2

The line perpendicular to y = 3x - 7 can be found by first determining what is the opposite reciprocal of the slope which is this case is 3

opposite reciprocal of 3 = - 1/3 

so my line is y = -1/3 x + b

to find b you plug in the point that the two line connect

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

Line: y = -1/3 x + 5