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

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?

How can I figure out the standard form of the equation of the line?
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!
Reply:You're welcome! Report It

Reply: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





===========





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..
Reply: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)
Reply: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 =%26gt; 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
Reply: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 %26amp; 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) %26amp; (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