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

Jun 20, 2015

The slope is $- \frac{5}{7}$

#### Explanation:

The slope of your line is $\frac{7}{5}$, therefore a director vector of your line is, for example, $\vec{A B} \left(5 , 7\right)$ (because the slope is $\frac{\Delta y}{\Delta x}$).

The vector $\vec{u} \left(- 7 , 5\right)$ is orthogonal with $\vec{A B}$ because dot product is null : $5 \setminus \times \left(- 7\right) + 7 \setminus \times 5 = 0$.

Finally, the slope is $\frac{\Delta y}{\Delta x} = \frac{5}{-} 7 = - \frac{5}{7}$.

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