Ineed 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.

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.

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

The range would be 13 because you’re finding the difference

8-2x+3x2=6 and six is your answer