# What is the equation of the line perpendicular to y=-2/21x  that passes through  (-1,6) ?

Mar 13, 2016

The slope of a perpendicular line is the negative reciprocal of the original line.

#### Explanation:

The slope of the perpendicular line is $\frac{21}{2}$, since the original line has a slope of $- \frac{2}{21}$.

Now we can use point slope form to plug in the point, the slope abs find the slope intercept form equation.

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

The point (-1,6) is $\left({x}_{1} , {y}_{1}\right)$ while m is the slope.

$y - 6 = \frac{21}{2} \left(x - \left(- 1\right)\right)$

$y - 6 = \frac{21}{2} x + \frac{21}{2}$

$y = \frac{21}{2} x + \frac{21}{2} + 6$

$y = \frac{21}{2} x + \frac{33}{2}$

Hopefully this helps!

Mar 13, 2016

$y = \frac{21}{2} x + \frac{33}{2}$

#### Explanation:

Given:$\text{ } y = - \frac{2}{21} x$ ..............................(1)

Compare to the standard form of$\text{ } y = m x + c$

Where
$m$ is the gradient
$x$ is the independent variable (can take any value you wish)
$y$ is the dependant variable. Its value depend on that of $x$
$c$ is a constant that for a straight line graph is the y-intercept

In your equation $c = 0$ the $\text{y-intercept } \to y = 0$

If $m$ is the gradient of the given line then $- \frac{1}{m}$ is the gradient of a line perpendicular to it.

$\textcolor{b l u e}{\text{So for the perpendicular line}}$

" "y_("perp") = (-1)xx(-21/2)xx x + c

color(blue)(" "y_("perp") = +21/2x + c)......................(2)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{To determine the value of } c}$

We know that this new line passes through$\left(x , y\right) \to \left(- 1 , 6\right)$

So substitute into equation (2) the values $\left(x , y\right) \to \left(\textcolor{g r e e n}{- 1} , \textcolor{m a \ge n t a}{6}\right)$

" "y_("perp") =color(magenta)(6) = +21/2(color(green)(-1)) + c......................(2_a)

$\textcolor{b l u e}{c = 6 + \frac{21}{2} = \frac{33}{2}}$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Putting it all together}}$

The line perpendicular to that given is: $y = \frac{21}{2} x + \frac{33}{2}$ 