# Write an equation of the line that passes through (1, -2) and is perpendicular to the line that....?

Write an equation of the line that passes through (1, -2) and is perpendicular to the line that passes through (4, 2) and (0, 4).

Any help would be appreciated very much. Thank you.

### 8 Answers

- 1 decade agoBest Answer
Use the forumula delta Y/ deltaX to find the slope of the given points

4-2/ 0-4 = -2/4 = -1/2

Since the perpendicular line is the equation y = -1/2x; the other equation has the slope of the negative reciprocal of -1/2x so the equation would be

y= 2x+b

then plugin x and y in this equation and you get

b= -4

so the final equation would be y=2x-4

Thats it

Source(s): My head - 1 decade ago
You must first find the slope of the line that passes through (4,2) and (0,4)

m = (4-2) / (0-4)

m = -1/2

Lines that are perpendicular have slopes that are negative reciprocals (flip, change the sign).

Thus, the slope of the line you are looking for will be 2.

You now have enough info to find the equation of your line:

m = 2

x = 1

y = -2

Using y = mx +b and our known values, we can solve for b

-2 = 2(1) + b

-2 = 2 + b

-4 = b

Therefore, your equation will be y = 2x - 4

- 1 decade ago
the equation of a line is y=mx+b where m is the slope and b is the y-intercept.

First, you find the equation of the line that passes through (4,2) and (0,4) by finding the slope which is the change in y/change in x which would be"

2-4/4-0

which equals -2/4 which is -1/2.

Since you're trying to find the slope of a line perpendicular to that, you use the negative reciprocal which means you switch the sign and flip the fraction, so your slope is 2/1 or 2.

Then to find the y-intercept, you use your point (1,-2) and plug it into the equation so it would read:

-2=2(1) +b

then solve for b

-2=2+b

-2-2=b

b=-4

so you're slope is 2 and your y-intercept is -4 so you put it into slope intercept form to get:

y=2x-4

- ErikaLv 43 years ago
first situation to do is rearrange the given equation into the form y = mx+c we've 5y - x = a million. upload x to the two factors ... 5y = x + a million Divide the two factors by ability of 5 ... y = (a million/5)x + a million/5 The gradient of the line is a million/5. the line perpendicular to this possible have a gradient of -5 (we take the unique gradient, turn it the different way up and negate it). this suggests the perpendicular could be written as y = -5x + c we don't comprehend 'c' i.e. the element the place the line crosses the y axis (it is likewise stated as the 'y intercept). to verify the value we only ought to plug in the values of the offered coordinate - that's why this is given to us ;-). In different words, exchange x to be a million and y to be -2 .... -2 = -5(a million) + c which provides c = 3 So the perpendicular equation is y = -5x + 3

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- Anonymous1 decade ago
first write the equation passing through points (4,2) and (0,4)

y = mx + b

where m (slope) = (y2-y1)/(x2-x1)=(4-2)/(0-4)= -1/2

then m = -1/2

so y=-1/2x + b knowing that the point (0,4) is on the line we replace x in y in the equation to get b: 4 = 0 + b so b=4

y=-1/2x + 4

the equation of the line y' = m'x' + b' that passes thru point (1, -2) we know that this line is perpendicular to y= - 1/2x+4

and we know that the product of the slopes of two perpendicular lines is -1

then m * m' = -1 so -1/2 m' = -1 then m'=2

so y' = 2x' + b' knowing that the point (1, -2) passes thru that line replce x and y in the equation to find b'

-2 = 2 + b' theb b'= -4

finally the equation is

y' = 2x' - 4

- 1 decade ago
slope of the line that passes through (4, 2) and (0, 4) = 4-2 / 0-4 = -1/2

slope of perpendicular line = 2

so eq. of desired line:

y+2 = 2(x-1)

'

- yupchageeLv 71 decade ago
line that passes through (4,2) & (0,4) has a slope of

(4-2)/(0-4)=-2

slope of perpindicular line has a slope of

-1/(-2)=1/2

y=.5x+b

-2=.5*1+b

b=-2.5

y=.5x-2.5b