How do you write the slope-intercept equation for the line that is perpendicular to the line 3x-5y=9 and that contains the point (2,-5)?

Jun 6, 2016

$y = - \frac{9}{5} x - 1 \frac{2}{5} , \text{ or } y = - \frac{9}{5} - 1.4$

Explanation:

First change the given equation into standard form, $y = m x + c$

$5 y = 3 x - 9 , \text{which gives } y = \frac{3}{5} x - \frac{9}{5}$

The slope is therefore $\frac{3}{5}$
The slope perpendicular to this is $- \frac{5}{3}$

Now, we have the slope of the required line as well as a point.

The easiest way to find the equation is to substitute these into the formula: $y - {y}_{1} = m \left(x - {x}_{1}\right)$

$y - \left(- 5\right) = - \frac{9}{5} \left(x - 2\right)$

$y + 5 = - \frac{9}{5} x + \frac{18}{5}$

$y = - \frac{9}{5} x - 1 \frac{2}{5} , \text{ or } y = - \frac{9}{5} - 1.4$