# What is the equation of the line perpendicular to y=-2x  that passes through  (4,-1) ?

Feb 26, 2016

$\text{ } \textcolor{g r e e n}{y = \frac{1}{2} x - 3}$

#### Explanation:

Suppose the slope (gradient) of the original equation was m. Then we would have: $y = m x$

The line perpendicular would have the gradient of $\left(- 1\right) \times \frac{1}{m}$

So for your equation $m = \left(- 2\right)$

That means that the line perpendicular will have the gradient of

$\left(- 1\right) \times \frac{1}{- 2} \text{ "=" } + \frac{1}{2}$
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So the new equation is: $y = \frac{1}{2} x$

The thing is that it should be $\textcolor{b r o w n}{y = \frac{1}{2} x + c}$

where c is a constant value
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$\textcolor{b l u e}{\text{To find the value of c}}$

We are given that $\textcolor{b l u e}{\left(x , y\right) \to \left(4 , - 1\right)}$
So by substitution we have:

" "color(brown)(color(blue)(-1) =1/2(color(blue)(4))+c

$\text{ } - 1 = 2 + c$

$\text{ } c = - 3$ giving

$\text{ } \textcolor{g r e e n}{y = \frac{1}{2} x - 3}$