An equation for a line which passes thru the point(1, -2)& which is perpendicular to the line given by (cont.)

Question

2x + y - 4 = 0 . - 4 = 0 .


Find an equation for a line which passes thru the point (1, -2) and which is perpendicular to the line given by 2x + y - 4 = 0 .

possible solutions

x - 3y - 7 = 0

x - y - 3 = 0

x - 2y - 5 = 0

x - 4y - 9 = 0

Answer 1

Given eqaution of straight line can be rewritten as can be
y = -2x +4,
The standard form of equation of line is y = mx + c where m is the slope of line and c is itercet on Y axis.
which means that its slope is -2.

For any line to be perpendicular to y = mx + c its slope should be -1/m i.e negative reciprocal of original line .

here it will be -1/-2 = 1/2

Now we have the slope, we can use the point and slope into the point-slope equation (y-y1) = m(x-x1) to get the equation

(y+2) = 1/2 (x-1)
y = 1/2x -5/2

-x +2y = -5

x - 2y -5 = 0

hence it matches 3rd option.

Answer 2

The slope of the line 2x + y - 4 = 0 is - 2.
The slope of the line perpendicular to 2x + y - 4 = 0 is (1/2).
So, the equation of the line passing through (1, - 2) and with slope (1/2) is : y+2 =(1/2) (x - 1) Or 2y + 4 = x - 1
which leads to x - 2y -5 = 0. Answer.
Verify:OK

Answer 3

Here's a little mantra for you:
For equations of lines, I want you to remember this word association.
Parallel = "same slope"
Perpendicular = "negative reciprocal"

2x + y - 4 = 0 means
y = -2x - 4, which means that the slope is -2 (y = mx + b form).

Since the slope of the equation of the given line is -2, it follows that the perpendicular slope will be the negative reciprocal. The negative reciprocal means you take the negative of the number by multiplying it by -1, and the reciprocal means you flip the fraction. In the case of -2, the negative reciprocal will be 1/2.

Therefore, our desired slope is 1/2.

Use the slope formula to get the equation of the line

(y2 - y1) / (x2 - x1) = m

Let m = 1/2. Let (1, -2) and (x, y) be (x1, y1) and (x2, y2) respectively.

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

Cross multiply, to get

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

2y + 4 = x - 1

Therefore, moving everything to the right hand side,

0 = x - 2y - 5

Answer 4

2x + y -4 = 0 can be changed to y = -2x +4, which means that its slope is -2. If the line you're finding is perpendicular, its slope is the negative reciprocal, 1/2.

Now that you have the slope, you can plug the point and slope into the point-slope equation (y-y1) = m(x-x1) to get the equation you're looking for.

(y+2) = 1/2 (x-1)
y = 1/2x -5/2

-x +2y = -5

x - 2y -5 = 0

So it would be the third choice

Answer 5

after manipulation of equation from 2x + y - 4 = 0,
y = -2x + 4
knowing y = mx + c
with m as the gradient of the line and c, the y-intersect,
gradient of perpendicular line is = 1/2 [ reciprocal of m ]

[[ the equation for finding an equation is: y - y1 = m(x - x1) ]]
y + 2 = 1/2 ( x - 1)
y = 1/2x - 2.5

multiply 2 on both sides of the equation,
2y = x - 5
manipulate the equation to be:
x - 2y -5 = 0

so the answer is the third one.

Answer 6

why could I. what's in it for me? i will no longer be able to have faith the form of people who think of somebody right it incredibly is purely going to do thier homework for them. all and sundry dumb adequate to think of that incredibly needs to learn extra.