Question

What lines are perpendicular to y=5x-3?

Answer 1

Perpendicular lines are lines that, when intersect the original line, form a right angle. This is formed when two lines' gradients are the negative reciprocals of each other.

In essence, $m_1 \cdot m_2 = -1$
Now let 5 be $m_1$
Thus, $5 \cdot m_2 = -1$

$m_2 = -\frac{1}{5}$

That means any line with a gradient or slope of $-\frac{1}{5}$ is a line that is perpendicular to this line.

In essence, the general equation would be: $y = -\frac{1}{5}x + C, C \in R$