Question

Are the following lines parallel?

y = -3x + 1

y = 4 - 3x

Answer 1

`Yes`

Explanation:

`We\ know\ that,\\For\ two\ equations\ of\ the\ form:\\\left \{ {a_1x+b_1y+c1=0} \atop {a_2x+b_2y+c2=0}} \right.\\to\ be\ parallel\ or\ have\ no\ solutions,(a_1)/(a_2)=(b_1)/(b_2) \\eq (c_1)/(c_2)\\So,\\Let's\ identify\ the\ coefficients\ of\ the\ terms\ in\ each\ equation:\\a_1=-3, a_2=-3 \\b_1=1, b_2=1 \\c_1=1, c_2=4 \\Hence,\\Let's\ now\ check\ the\ ratio\ of\ the\ corresponding\ coefficients:\\(a_1)/(a_2)=(-3)/(-3)=1\\(b_1)/(b_2)=(1)/(1)=1\\`

`(c_1)/(c_2)= (1)/(4) \\We\ hence,\ deduce\ that :\\(a_1)/(a_2)=(b_1)/(b_2)\\eq (c_1)/(c_2)\\Hence,\\The\ two\ lines\ are\ parallel.`