Is 7x=4y+1 and -14x+18y=1 perpendicular or parallel

The first step to answering this question is to find the slope of the first line. To do that, we need to put it in slope-intercept form.
-7x - 4y = -4 => -4y = 7x - 4 => y = (-7/4)x + 1.
So the slope of this line is -7/4. Perpendicular lines have a negative reciprocal slope, so the slope of the perpendicular line is 4/7. Using that and the point (-14, -3) we can make an equation for the line in point-slope form: y + 3 = (4/7)(x + 14) . We can then convert this into slope intercept form.
y + 3 = (4/7)(x + 14) => y + 3 = (4/7)x + 8 => y = (4/7)x + 5.

So your final answer is y = 4/7 x + 5