Answer:
x -4y = -24
Explanation:
Given the equation of a line in standard form, you can write the equation of the perpendicular line by swapping the coefficients and negating one of them. The constant needs to be adjusted to make the equation true at the point you want the line to pass through.
4x +y = 7 . . . . given line
x -4y = constant . . . . equation with coefficients swapped, one negated
x -4y = (-4) -4(5) = -24 . . . . equation with appropriate constant
An equation for the desired line is ...
x -4y = -24
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Additional comment
The standard form equation has a positive leading coefficient, so the choice of which coefficient to negate will take that into account.
The slope of the standard form line ...
ax +by = c
is m = -a/b.
The slope of the perpendicular line is the opposite reciprocal of this:
m' = -1/m = b/a
You can see that this swaps the coefficients and negates one of them.