Determine if the line that passes through the points ( -2, -10) and (6, -1) is parallel, perpendicular or neither to the line specified  by 7 y - 9 x = 15 .

Solution

Togive answer this we'll require the slopes of the two lines.  As we have two pointsfor the first line we can employ the formula for the slope,

m ₁       =-1 -( -10)/6-(-2)=     9/8

Actually we don't need the equation of this line and thus we won't bother with it.

Now, to get the slope of the second line all we have to do is put it into slope-intercept form.

7 y = 9 x + 15

            y =       (9/7 )x +(15/7) ⇒   m₂  = 9/7

Okay, as the two slopes aren't the similar (they're close, but yet not the same) the two lines are not parallel.  Also,

 (9 /8) (9 /7) = 81/56 ≠ -1

So the two lines aren't perpendicular either.

Thus, the two lines are neither parallel nor perpendicular.