Mathematics: 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

400Step-by-step explanation:...

Write an equation of the line through(2-1) and

Ответ:

richellemjordan

13.03.2022

Mathematics

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

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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

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