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Perpendicular lines have gradients whose product is −1, so the new gradient is the negative reciprocal −1/m. Substituting the given point then fixes the intercept.
Perpendicular gradient
m₁ · m₂ = −1, so m₂ = −1 / m₁
The new gradient is −0.25, so c = 5 + 2 = 7 and the line is y = −0.25x + 7.
They are perpendicular to each other, but the product rule breaks down because a vertical line has no defined gradient.