What is the equation of the line perpendicular to y=9/20x  that passes through  (-1,-5) ?

Apr 27, 2018

Find the negative reciprocal of the slope of our given equation,
$y = \frac{9}{20} x$.

Keep in mind that the slope of any line is defined as the negative reciprocal of the slope of the line that it is perpendicular to.

The negative reciprocal of $\frac{9}{20}$ is $- \frac{20}{9}$. This is the slope of our perpendicular line.

This perpendicular line also lies on the point (-1, -5). With the coordinates of this point and the slope we previously found, we can construct our answer in point slope form:

$y - {y}_{1} = m \left(x - {x}_{1}\right)$, where m = slope, ${x}_{1}$ and ${y}_{1}$ are the x and y-coordinate of the point (${x}_{1}$, ${y}_{1}$) respectively.

In our case, m = $- \frac{20}{9}$, ${x}_{1}$ = -1, and ${y}_{1}$ = -5.

Now all we must do is to simply plug in our values:
$y + 5 = - \frac{20}{9} \left(x + 1\right)$

If the question requires an equation in slope-intercept form, simply subtract 5 from both sides and simplify!