SOLUTION: What is the equation of the line perpendicular to the line x-4y=6 through (3,5) in slope intercept form?

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Question 526780: What is the equation of the line perpendicular to the line x-4y=6 through (3,5) in slope intercept form?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The equation given for the first line is
x-4y=6
The slope intercept for for the first line is
y=%281%2F4%29x-3%2F2
The slope of that line is 1%2F4
Slopes of perpendicular lines multiply to give you -1
so the slope of a perpendicular line will be
m=-4=%28%28-1%29%29%2F%28%281%2F4%29%29
Maybe you could say that for a point (x,y) in the perpendicular line, the slope of the line passing through that point and (3,5) is
m=-4=%28y-5%29%2F%28x-3%29
and work from there to the slope-intercept form.
Or maybe you are supposed to follow the recipe for the case when you have the slope and a point and write the point-slope form of the equation as
m=-4=%28y-5%29%2F%28x-3%29
and work from there to the slope-intercept form:
y=-4x%2B7
Some teachers like to see you follow recipes for solving problems. Others enjoy seeing a variety of ways to solve a problem.