How can I figure out the standard form of the equation of the line?

Question

The two points are (-6,-2) and (6,-4) and the slope is -1/6. How can I put this in standard form Ax+By=C?

Answer 1

Point-slope formula:
y-y1=m(x-x1)
y+2=-1/6(x+6)
y+2=-1/6x-1
y=-1/6x-3

In Standard form:
Multiply both sides by 6:
6(y)=6(-1/6x-3)
6y=-x-18

Add x from both sides:
x+6y=-18

Check:
-6+6(-2)=-18
-6-12=-18
-18=-18

6+6(-4)=-18
6-24=-18
-18=-18

I hope this helps!

Answer 2

First, determine the equation to be used. We can use y=mx+b where m is the slope and b is the y-intercept.

Second, use any of the two pairs of coordinate to determine the y-intercept. Since the two pairs lie on the same line, any of the two pairs can be used. Let us use (6, -4)

y = mx+b
substitute the values for y, x and m,
(-4) = (-1/6)(6) + b

multiply -1/6 and 6
(-4) = (-1) + b

b + (-1) = (-4)

by adding (+1) to both sides we have,
b = -4 + 1

b = -3

therefore the y-intercept is -3....

Third, to form the equation, plug in the values of m and b,

y = mx + b
y = (-1/6)x + (-3)

multiply both sides by 6 to change all the numerical coefficients to integers..

6y = -x + (-18)

by adding (+x) to both sides we have,
6y + x = -18

or by commutative property,

x+6y = -18

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to check, plug in the two pairs of coordinates to our equation,

using (-6, -2)

x + 6y = -18
(-6) + 6(-2) = -18
(-6) + (-12) = -18
-18 = -18 since both sides are equal, the equation is true for coordinates (-6, -2)

using (6, -4)
x + 6y = -18
(6) + 6(-4) = -18
6 + (-24) = -18
-18 = -18 since both sides are equal, the equation is true for coordinates (6, -4)


since the equation is true for both the given pairs of coordinates, then our equation is correct..

Answer 3

y = ax + b
wher a is the slope
so y = -1/6 x + b
if y = -2 then x = -6 so replacing in the above equation
-2 = (-1/6)(-6) + b
-2 = 1 + b => b=-3
the equation is y = -1/6x -3
checking we replace the coordinates of the point (6,-4) into the equation we just found
we get
y = (-1/6)(6) - 3 = -4 so it's OK

in the standard form we get
-1/6 x -y = 3

Answer 4

well for any line the equation should go like :

y = mx + c

if you have two known points, substitute with their values at the above equation and get m & c values

for the example given by you
the two points are (-6,-2), (6,-4)

substituting with the first points :

-2 = -6m + c ---(1)

substituting with the second point :

-4 = 6m + c ---(2)

now solve (1) & (2) simultaneously to get the values of m and c..
I'd rather adding them to each other, therefore;

-2-4 = -6m + c + 6m + c

-6 = 2c

c = -3

now you can substitute with the value of c at either (1) or (2) to get m in case you don't have it..but you already know it's -1/6

so the equation of the line should be

y = (-1/6) x - 3 (multiply the whole equation by 6)

6y = -x - 18

therefore

x + 6y = -18

Answer 5

standard form is Y=mX + b where m = slope and b = Y intercept

plug your co-ords and slope in

(y-y1) = m(x-x1)
y-y1 = mx - mx1
y = mx - mx1 +y1
y = mx + (y1-mx1)
y = mx + b let b = (y1 - mx1)