Question 526780
The equation given for the first line is
{{{x-4y=6}}}
The slope intercept for for the first line is
{{{y=(1/4)x-3/2}}}
The slope of that line is {{{1/4}}}
Slopes of perpendicular lines multiply to give you {{{-1}}}
so the slope of a perpendicular line will be
{{{m=-4=((-1))/((1/4))}}}
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=(y-5)/(x-3)}}}
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=(y-5)/(x-3)}}}
and work from there to the slope-intercept form:
{{{y=-4x+7}}}
Some teachers like to see you follow recipes for solving problems. Others enjoy seeing a variety of ways to solve a problem.