Question

Write an equation of the line through(2-1) and perpendicular to 2yx-4 Write the equation in the form x The one the Enter your answer in the box and then click Check Answer parts showing i Type here to search

Answer 1

Answer:

$2x+y=3$

Step-by-step explanation:

Here we aer given a point (2,-1) and a line $2y=x-4$. We are supposed to find the equation of the line passing through this point and perpendicular to this line.

Let us find the slope of the line perpendicular to $2y=x-4$

Dividing above equation by 2 we get

$y=\frac{1}{2}x-2$

Hence we have this equation in slope intercept form and comparing it with

$y=mx+c$ , we get Slope $m = \frac{1}{2}$

We know that product of slopes of two perpendicular lines in -1

Hence if slope of line perpendicular to $y=\frac{1}{2}x-2$ is m' then

$m\times m' =-1$

$\frac{1}{2} \times m' =-1$

$m'=-2$

Hence the slope of the line we have to find is -2

now we have slope and a point

Hence the equation of the line will be

$\frac{y-(-1)}{x-2}=-2$

$y+1=-2(x-2)$

$y+1=-2x+4$

adding 2x and subtracting  on both sides we get

$2x+y=3$

Which is our equation asked