Which one is right?

Question

Find an equation of a line that passes through the point (4,2) and is perpendicular to the line with the equation

5X-4Y=8

My teacher marked it wrong on my test, can someone answer so i can see if I actually got it right?

i was missing the - on the slope

Answer 1

Sure. i'll give a brief explan. cuz it doesnt look like you're that confused.

point slope: m(x-x1)=y-y1
m=-4/5, x1=4, y1=2
-4/5*(x-4)=y-2
-4x/5+16/5=y-2
y=-4x/5+26/5

If you got a different answer from mine, make sure your signs are right! it's easy to get the signs mixed up.

Answer 2

The line perpendicual to 5x-4y = 8

has the form 4x+5y = c
where c is constant
as product of slopes should be -1

it passes through (4,2)

SO 4*4 + 5*2 = c or c = 26
so equation = 4x+5y = 26

Answer 3

5x - 4y = 8
-4y = -5x + 8
y = 5/4 y - 2

m1 = 5/4 ----> m2 = -4/5
using slope intercept
y = mx + b
2 = (-4/5)* 4 + b
2 = -16/5 + b
therefore
b = 2 + (16/5)
= 26/5

therefore the line perpendicular is
y = -4/5 x + 26/5
5y = -4x + 26
5y + 4x = 26

sufficient?

Answer 4

5x-4y=8
-4y=-5x+8
y=5/4x-2

slope = 5/4
slope perpindicular = -4/5

y-y1-m(x-x1) This is point-slope equation of line where m=slope and (x1,y1) is the point through which our line must go.

So...

y-2=-4/5(x-4)
This is one way of writing the line in question. We can also solve for y and write in slope-intercept form.

y-2=-4/5(x-4)
y-2=-4/5x+1/5
y=-4/5x+26/5

Hope this has helped.
By the way, what did you end up getting that your teacher marked wrong?

Answer 5

Well an easy way is to convert it to Y=mX+b format.
where m is the slope.

5X - 4Y = 8
4Y = 5X - 8
Y = (5/4)X - 2
Slope = 5/4

now, to make it perpendicular you negate it and inverse it.

Which makes -4/5

Now we have Y = (-4/5) X + b

If you plug in 4 for X and 2 for Y:

2 = (-4/5) 4 + b
2 = -16/5 + b
2 + 16/5 = b
10/5 + 16/5 = b
26/5 = b

Y = -4/5 X + 26/5

Answer 6

put the equation to y=mx+b form, and you get:
-4y=-5x+8
divide by -4 and you get
y=5x/4 +2
sin ce you're finding the equation of the line perpendicular, the slope of the line you're trying to find is the negative inverse of 5/4, so it's -4/5

so the equation of that line is y=-4x/5+b

maybe you got it wrong b/c you didn't put it in a specified form?

Answer 7

.

m(x-x1)=y-y1
m=-4/5, x1=4, y1=2
-4/5*(x-4)=y-2
-4x/5+16/5=y-2
y=-4x/5+26/5