How do you write #y = 1/2x-1# in standard form?

Question

Eva Abramson · Accepted Answer

See a solution process below:

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 First, multiply each side of the equation by #color(red)(2)# to eliminate the fraction and ensure all of the coefficients are integers as required by the formula while keeping the equation balanced: #color(red)(2) * y = color(red)(2)(1/2x - 1)# #2y = (color(red)(2) * 1/2x) - (color(red)(2) * 1)# #2y = 2/2x - 2# #2y = 1x - 2# Next, subtract #color(red)(1x)# from each side of the equation so the #x# and #y# terms are on the left side of the equation while keeping the equation balanced: #-color(red)(1x) + 2y = -color(red)(1x) + 1x - 2# #-1x + 2y = 0 - 2# #-1x + 2y = -2# Now, multiply each side of the equation by #color(red)(-1)# to make the #x# coefficient non-negative as required by the formula while keeping the equation balanced: #color(red)(-1)(-1x + 2y) = color(red)(-1) * -2# #(color(red)(-1) * -1x) + (color(red)(-1) * 2y) = 2# #color(red)(1)x + color(blue)(-2)y = color(green)(2)# #color(red)(1)x - color(blue)(2)y = color(green)(2)#

Avery Alexander · Answer

undefined To write $ y = \frac{1}{2}x - 1 $ in standard form, move all terms to one side of the equation and set it equal to zero. Multiply both sides by 2 to eliminate the fraction. Rearrange the terms so that the variables are on one side and the constants on the other side. The standard form of the equation will be: $ 2y - x + 2 = 0 $.