# What is the equation of the line perpendicular to  y=-3/7x+12  at x=-1 ?

Apr 2, 2017

$y = \left(\frac{7}{3}\right) x + \left(\frac{310}{21}\right)$

#### Explanation:

Perpendicular means that the slopes will be opposite, so the slope is (7/3). At x = -1 the original line y value is $12 + \frac{3}{7}$ or $\left(\frac{87}{7}\right)$.
To find the new constant at that point we put it into the new equation.
$y = \left(\frac{7}{3}\right) x + b$ ; $\left(\frac{87}{7}\right) = \left(\frac{7}{3}\right) \left(- 1\right) + b$ ; $\left(\frac{87}{7}\right) + \left(\frac{7}{3}\right) = b$ ; $\left(\frac{261}{21}\right) + \left(\frac{49}{21}\right) = b$

$\left(\frac{310}{21}\right) = b$
So the new line equation is $y = \left(\frac{7}{3}\right) x + \left(\frac{310}{21}\right)$

CHECK: At (-1, (87/7)) $\left(\frac{87}{7}\right) = \left(\frac{7}{3}\right) \left(- 1\right) + \left(\frac{310}{21}\right)$

$\left(\frac{87}{7}\right) = - \left(\frac{49}{21}\right) + \left(\frac{310}{21}\right)$ ; $\left(\frac{87}{7}\right) = \left(\frac{261}{21}\right)$
$\left(\frac{87}{7}\right) = \left(\frac{87}{7}\right)$ Correct!