Explanation:
I think you mean you need the equation in slope-intercept form :
y = ax + b
"a" being the slope, "b" being the y-intercept value (the y-value when x = 0).
the slope is always the ratio of
y coordinate difference / x coordinate difference
when going from one point on the line to another.
a perpendicular slope turns this ratio upside-down and flips the sign :
- x coordinate difference / y coordinate difference
so, first let's bring the given line to a slope-intercept form too to get its parameters :
x + 4y = 12
4y = -x + 12
y = -x/4 + 12/4 = -x/4 + 3
so, the slope of the given line is -1/4.
the perpendicular slope is then - -4/1 = 4.
now we have the slope of the requested line. to get the y-intercept we use the given point :
-6 = 4×-1 + b = -4 + b
-2 = b
so, our full equation is
y = 4x - 2