Question

20pts! What is the equation of a line that is parallel to x 2y= 4 and passes through the point (0, 0)? Please explain your answer! Thanks!

Answer 1

The symbol between the x and 2y is missing. If it is a plus sign, then 

Anything parallel to x+2y = 4 is going to be of the form x+2y = C where C is some fixed number. The left side stays identical and unchanged. To find the value of C, we plug in (x,y) = (0,0). So replace x with 0 and replace y with 0

x+2y = C
0+2*0 = C
0 + 0 = C
0 = C
C = 0

So the equation of the parallel line is x+2y = 0

Again this is all hinged on the assumption that there is a plus sign between x and 2y

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If the symbol between the x and 2y is a minus sign then

Anything parallel to x-2y = 4 is in the form x-2y = C where C is a constant

Plug in (x,y) = (0,0)
x-2y = C
0 - 2*0 = C
0 - 0 = C
0 = C
C = 0
So the parallel equation is x-2y = 0 only if the symbol between the x and 2y is a minus sign.