TEST tomorrow, please help!!!!!!!!!!!!!!!!!!! The intersection point of 2 perpendicular lines lies on the.....

Question

x-axis. the equation of one line is
x+2y + 4 = 0. Determine the equation of the other line.
(ok, the answer is 2x-y = -8, but I need to know how to do it. thank you very much!)

Answer 1

x+2y + 4 = 0 crosses the x-axis at x = -4.
The slope of this line is -1/2, so the slope of the perpendicular line is 2, and the equation of the line is
y = 2(x + 4)
y = 2x + 8
2x - y = - 8

Answer 2

The product of the slopes of two perpendicular lines is -1. If m1, m2 are the slopes -1/2xm2= -1 or m2=2. The slope of the perpendicular is 2. Since the intersection of two perpendiculars lies on the x-axis (0, -4) are points on the perpendicular.The equation for the line is Y-0/x-(-4)=2
or y=2x + 8 ie2X-Y=-8

Answer 3

The slopes of two perpendicular lines are opposite reciprocals of one another. So, if the slope of one line is 3/5, the slope of the perpendicular line is -5/3.

The line perpendicular to x + 2y + 4 =0 is the line with a slope that is the opposite reciprocal of the slope of this line. Solve the equation for y to put the equation in slope-intercept form.
x + 2y + 4 = 0
2y = -x - 4
y = -(1/2)x - 2

So, the slope of the perpendicular line to this is 2.

The point of intersection is the x-intercept of both lines.
0 = -(1/2)x - 2
2 = -(1/2)x
-4 = x

So, the equation of the line perpendicular to x + 2y + 4 = 0 that passes through the point (-4, 0) is
y - 0 = 2(x - (-4)), by the point-slope form of the equation of a line
y = 2(x+4)
y = 2x + 8
So, 2x - y + 8 = 0

Answer 4

Put the first line in slope-intercept form to get
y = -.5x - 2
Now, the slope (m) of the line is -.5 so the slope of a line perpendicular to it is -1/m or 2 so the equation of the 2'nd line will be
y = 2x + b
How to determine the b? Look at the first equation. The problem says the two lines intersect on the x-axis (where y is 0) so what is the x value there? x = -4. Now plug in 0 and -4 for the y and x values in the equation for the 2'nd line and solve for b
0 = 2(-4) + b
0 = -8 + b
b = 8
And the equation of the 2'nd line is
y = 2x + 8

HTH

Doug

Answer 5

Rather quickly ( since being on the x-axis means y = 0) you can determine that x must be - 4, so (-4,0) is the intersection point of your perpendiculars.

From triggering with your line equation you get another form of the line: y = (-x - 4)/2 or (-1/2)x - 2 which tells you your given line has slope (-1/2). That implies the perpendicular line has slope 2 (negative reciprocal of given-line-slope).

Knowing slope and a point (on your perpendicular) your new line (perpendicular to given line) thru (-4, 0) is
y-0 = 2 [x-(-4)] which you can trigger around to the form you gave in your problem.
- - - - - - -
BTW, I personally favor slope-intercept form over other forms; to me it's easier to graph the line from that form.

Answer 6

Rearrange x+2y+4=0 to y=mx+c
thus,
2y=-x-4
y=-1/2x-2 where m=-1/2 (gradient) and c=-4 (y-intercept)

As the 2 perpendicular line intersect at x-axis, y=0
When y=0,
0=-1/2x-2, x=-4

For perpendicular lines, grad of another line is -1/ (grad of the 1st line)

Thus the grad of the 2nd line is , -1/(-1/2)=2

Using y =mx+c with y=0 and x=-4 and grad =2,
we can find y-intercept
0=2(-4)+c
c=8

Thus the line is y=2x+8
Rearrangin it, we get 2x-y=-8

Answer 7

okay, what you do is you know that any point on the x-axis is goign to have a y-coordinate of 0. so plug in zero for y and solve for x. okay, now you have a an ordered pair, (0,-4) now, plug this into point slope format, which is y-y1=m(x-x1), where m is the slope
now, since it is perpendicular, u need to take the opposite reciprocal of the original slope, so u take -1/2, reverse it to
-2/1 and then mulitply by -1 to get 2 as a slope. now plug in the stuff. (y-0)=2(x+4)or y =2x+8, which becomes 2x-y=-8 if you shift things around

Answer 8

y = -1/2 x + 2
two line are perpendicular if m * m' = -1
m' = -1/(-1/2) = 2

so the eq. will be:
y = 2x + b

now we know that both lines intersect on the x axis so the point of intersection has y = 0
in the first equation replace y by 0 : x = 4
so the point of intersection is (4, 0)
this point belongs to the new line too so replacing x and y we get b
0 = 2*4 + b
b = -8

the eq. will be:
y = 2x - 8

Answer 9

first of all you need to find it's reciprocal right? right.
then figure out where the first line hits the x-axis and make the second equation pass the same point.
i hope i'm right lol