Determine whether the graphs of the given equations are parallel, perpendicular, or neither.

Y - 4 = 3 (x + 2)

2x + 6y = 10

When the slopes are equal, the two lines are parallel.

When the product of two slopes is - 1, then the two lines are perpendicular.

So, y - 4 = 3x + 6;

Then, y = 3x + 10; the slope of the first line is 3;

2x + 6y = 10;

Then, 6y = - 2x + 10;

y = (-2/6) x + 10/6;

Finally, y = (-1/3) x + 5/3; the slope if the second line is - 1/3;

Because 3 * (-1/3) = - 1 the two lines are perpendicular.