# what is the equation of the line passing through the point (-2, -3) and is perpendicular to the line 4y + x = 6

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point = (-2,-3)

equation of line perpendicular to it = 4y + x = 6

= y + x/4 =3/2

= y = -x/4 + 3/2

Therefore slope = -1/4 as y =mx + c where m is slope

lines are perpendicular. Therefore, product of slope = -1

m.m1 = -1

= m x -1/4 = -1

= m = 4

hence slope of line passing through (-2,-3) is 4

now , y-y1=m(x-x1)

= y-(-3)=4(x-(-2))

= y+3=4(x+2)

= y+3=4x+8

= y=4x+5

The given equation of the line is `4y+x=6.`

Rearranging it in the slope-intercept form, i.e. `y=mx+b` where `m` denotes the slope of the line we get:

`4y=-x+6`

Dividing both sides by 4;

`y=-1/4x+6/4`

`rArr y=-1/4x+3/2`

Thus the slope of the given line, `m=-1/4` .

The slope of a perpendicular line will be the negative reciprocal of the slope of the original line.

Hence, slope of the perpendicular line =` 4` .

Now, to find the equation of the perpendicular line we will use the point-slope form of the equation of the straight line i.e. `y-y_1=m(x-x_1)` where `(x_1,y_1)` is a known point on the line, `m` is the slope of the line and `(x,y)` is any other point on the line.

Here, `(x_1,y_1)=(-2,-3)` and `m=4` .

Hence, the equation of the perpendicular line is given by:

`y-(-3)=4[x-(-2)]`

`rArr y+3=4(x+2)`

`rArr y+3=4x+8`

`rArr 4x-y=-5`

Therefore, the required equation of the line passing through the point `(-2, -3)` and perpendicular to the line `4y + x = 6` is **4x-y=-5**.

(-2, -3) and a perpendicular line to 4y+X=6 turn this into y=mx+b equation

you would get: 4y+x=6

4y=-X+6

y=(-1/4)x+6

where -1/4 is your slope and 6 is your y intercept, now we know that when its perpendicular we find the opposite reciprocal , which in this case is 4.

so we know that our new equation has a slope of 4

so y=4x+b then plug in -2, -3 into x and y.

-3=4(-2)+b

-3=-8+b

5=b

so it would be:

y=4x+5

(-2, -3) and a perpendicular line to 4y+X=6 turn this into y=mx+b equation

you would get: 4y+x=6

4y=-X+6

y=(-1/4)x+6

where -1/4 is your slope and 6 is your y intercept, now we know that when its perpendicular we find the opposite reciprocal , which in this case is 4.

so we know that our new equation has

point (-2, -3) and is perpendicular to the line 4y + x = 6

The slope of your line is -1/4. The slope of your perpendicular line is the negative reciprocal which is 4.

Plug these values into the point slope formula:

y - y1 = m(x - x1) to get

y + 3 = 4(x + 2)

You can leave it in that form or change to whichever form you please.