First, we can use the point-slope formula to find an equation for this line. The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))#
Where #color(blue)(m)# is the slope and #color(red)(((x_1, y_1)))# is a point the line passes through.
Substituting the values from the problem gives:
#(y - color(red)(1)) = color(blue)(1/2)(x - color(red)(3))#
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
We can transform our equation into the standard form as follows:
First, multiply each side of the equation by #color(red)(2)# to eliminate all fractions while keeping the equation balanced:
#color(red)(2)(y - color(red)(1)) = color(red)(2) xx color(blue)(1/2)(x - color(red)(3))#
#(color(red)(2) xx y) - (color(red)(2) xx color(red)(1)) = x - color(red)(3)#
#2y - 2 = x - 3#
Next, subtract #color(red)(x)# and add #color(blue)(2)# to each side of the equation to put the #x# and #y# terms on the left side of the equation while keeping the equation balanced:
#-color(red)(x) + 2y - 2 + color(blue)(2) = -color(red)(x) + x - 3 + color(blue)(2)#
#-x + 2y - 0 = 0 - 1#
#-x + 2y = -1#
Now, multiply each side of the equation by #color(red)(-1)# to convert the #x# coefficient to a positive integer while keeping the equation balanced:
#color(red)(-1)(-x + 2y) = color(red)(-1) xx -1#
#(color(red)(-1) xx -x) + (color(red)(-1) xx 2y) = 1#
#color(red)(1)x - color(blue)(2)y = color(green)(1)#
