How do you write #1/3x-1/3y=-2# in standard form and what is A, B, C?

↳Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
1 Answer
smendyka
Feb 7, 2017

#color(red)(1)x - color(blue)(1)y = color(green)(-6)#

Explanation:

The standard form of a linear equation is: #color(red)(A)x + color(blue)(B)y = color(green)(C)#

where, if at all possible, #color(red)(A)#, #color(blue)(B)#, and #color(green)(C)#are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

To transform this equation into standard form we need to multiply each side of the equation by #color(red)(3)# which will also keep the equation balanced:

#color(red)(3)(1/3x - 1/3y) = color(red)(3) xx -2#

#(color(red)(3) xx 1/3x) - color(red)(3) xx 1/3y) = -6#

#3/3x - 3/3y = -6#

#1x - 1y = -6#

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