help with the Ax+By=c form?

Question

(6,1) (5,4)
i had to put this in Ax+By =C and reduce to the lowest term

my answer is y=3x+19 but its wrong.i only have
7 spaces for my whole complete answer.

same with this
(7,-3)(4,-8)

Answer 1

y = mx + c is the standard equation of line in which

m = slope of the line
c = intercept made by the line on the yaxes

and when two points are given say (x1,y1) and (x2,y2)
than
m = y2-y2 / x2-x1

After getting the value of m just put that into the general equations.

Now ur cases

Case 1

(6,1) , (5,4)

m = (4-1)/(5-1) = 3/-1 = -3

So now just put the value into the general equation of staright line

so answer is y = -3x + c

Now since this is the equation which we have got using
(6,1) , (5,4) so that means that both these points lie on the line so if we plug in any one point into the equation than it must satisfy that and we can be able to find our value of c and hence the answer

so letz us ( 6,1) so just put x=6 and y=1 { u will get the same answer even if u will use x and y as 5 and 4}

so by putting the vales in the equation we got

y = -3x +c

1 = -3 (6) + c
1 = -18 +c
c = 19

y = -3x +19 --- Tats the answer ...............!!!!!!


Case 2

(7, -3) , (4,-8)

m =[ -8- (-3)] / [4-7] = -5 / -3 = 5/3

so y = 5/3 (x) + c

now put any point out of (7, -3) , (4,-8) in the equation we have got to get the value of c letz use (4,-8 ) this time

-8 = 5/3 * 4 +c
-8 = 20/3 + c
c = -8 - 20/3

c = -44/3

so equation is y = 5/3 x -44/3
multiply both sides by 3

3y = 5x-44 -- Thats the answer for the second case

Answer 2

Y= mX + b is the standard form for a straight line. To fnd the equation for ANY straight line, you need 2 pieces of information: the line's slope and a point on the line

For your first problem, (6,1)(5,4), you have all the information you need. The line's slope is the letter m in the equation and slope is defined as rise/run. In plain English, it means "how much did height change over a given distance?". We calculate this as
(4-1)/(5-6), =3/-1, or -1/3
Your equation so far looks like this: y = -1/3x + b
Now, use either one of the two given points to find b.
The rationale here is that since (6, 1) lies on the line it must satisfy the equation. I plug in 6 for x and 1 for y to get 1=(-1/3)(6)+b, or 1 =-2 + b, or b=3
The final equation you seek is y=(-1/3)x + 3.

Leaving the equation in this form immediately tells you the slope of the line( it's -1/3, and the - sign tells me it leans to the left), and the line cuts across the
y-axis at (0,3). NOTE:! This holds true ONLY IF y is +1y, and all by itself on one side of the equation.
I see you wanted this in the form Ax + By =C

OK y=(-1/3)x +3 becomes 3y = -x +9, x+3y=9

Your second problem gets handled in exactly the same way.
m=(-8 -(-3))/(4-7), -5/-3, =5/3
y=(5/3)x + b
Substitute 7&-3 for x and y, -3=(5/3)7 + b
-3=35/3 + b, from which b= -3 -35/3 =-9/3 -35/3
=-44/3
y=(5/3)x -44/3.
In Ax + By =C form, 3y=5x-44, 5x -3y =44

I hope this helps. I appreciate the fact that you tried. I feel my time explaining the procedure to you is not wasted. Good luck!

Answer 3

Question 1
m = 3 / (- 1) = (- 3)
Use point (6 , 1)
y - 1 = (- 3) (x - 6)
y = - 3x + 19
3x + y = 19

Question 2
m = ( - 8 + 3) / (4 - 7)
m = (- 5) / (- 3) = 5 / 3
Use point (7 , - 3)
y + 3 = (5/3) (x - 7)
3y + 9 = 5x - 35
5x - 3y = 44

Answer 4

Actually, the first form is y=19-3x

The second form is y=(-44+5x)/3

Answer 5

i get (y-1)= -3(x-6)

y-1=-3x+18

3x+y=19 7 spaces


(-8-(-3))/(4-7)=-5/-3=5/3

y+8=5/3(x-4)

3y=5x-48

5x-3y=48

Answer 6

m=(4-1)/(5-6)=-3
y=mx+b
1=-3(6)+b
1=-18+b
19=b
y=-3x+19
or 3x+y=19