determine the following lines are parrallel? x-y+1=0 6x-6y+7=0

determine the following lines are parrallel ?     x-y+1=0       6x-6y+7=0

$$\boxed{ \textcolor[rgb]{1,0,0}{a} *x + \textcolor[rgb]{0,0,1}{b} *y + c = 0 \qquad m = -\frac{ \textcolor[rgb]{1,0,0}{a} }{ \textcolor[rgb]{0,0,1}{b} } } \\$$

$$\\ \textcolor[rgb]{1,0,0}{1} *x \textcolor[rgb]{0,0,1}{-1} *y +1 = 0 \qquad m = -\frac{ \textcolor[rgb]{1,0,0}{1} }{ \textcolor[rgb]{0,0,1}{(-1)} } = 1 \\ \\ \textcolor[rgb]{1,0,0}{6} *x \textcolor[rgb]{0,0,1}{-6} *y +7 = 0 \qquad m = -\frac{ \textcolor[rgb]{1,0,0}{6} }{ \textcolor[rgb]{0,0,1}{(-6)} } = 1 \\$$

The lines are parrallel because m is equal.

Parallel lines have the same slope..let's put both equations in the form  y = mx + b, where "m" is the slope of the line......so we have

x-y+1=0  →  y = x + 1

6x-6y+7=0 → 6y = 6x + 7 → y = x + 7/6

And since the coefficient in front of both "x's" in the two equations is the same (an understood "1" )...the slopes are the same ....thus....they are parallel...