determine whether the pair of lines are parallel, perpendicular, or neither

Question

6x=7y=1

-30x=35y=1

Answer 1

I'm assuming that the equations are:

(1) 6x - 7y = 1 and

(2) -30x - 35y = 1.

If two slopes are parallel then they will have the SAME SLOPE. If they are parallel, then their slopes are OPPOSITE RECIPROCALS of each other. Thus, the whole point of this exercise is to find the slopes of each line first.

So, we'll put each equation back into y = mx + b. For equation (1) we have

6x - 7y = 1

-7y = 1 - 6x

y = -1/7 + 6/7x

Hence the slope of this line is 6/7

For equation (2)

-30x - 35y = 1

-35y = 1 + 30x

y = -1/35 - 30/35x

Hence the slope of this line is -30/35 = -6/7

Thus, the two slopes are not the same → they are not parallel

The two slopes are not opposite reciprocals of each other, because if they were, one number is 6/7 whereas the other would be -7/6 (or -6/7 and 7/6) → they are not perpendicular either.

Hence, the two lines are neither.

If the equations are incorrect, just follow the procedure posted above and figure out if the slopes are the same or are opposite reciprocals of each other.

Hope this helps

Mr. K