Question

How do you find the slope of a line perpendicular to `y=7/5x-2`?

Answer 1

The slope is `-5/7`

Explanation:

The slope of your line is `7/5`, therefore a director vector of your line is, for example, `vec{AB} (5,7)` (because the slope is `(Delta y) /(Delta x)`).

The vector `vec{u} (-7,5)` is orthogonal with `vec{AB}` because dot product is null : `5 \times(-7) + 7\times 5 = 0`.

Finally, the slope is `(Delta y) /(Delta x) = 5/-7 = - 5/7`.

Remark. You need orthonormal system for the equation of the line. But I suppose it is :-)