determine whether the graphs of the pair of equations are paralndicular or neither?

Question

4x + 5y=2 and 5x-4y=1

Answer 1

They will be perpendicular. You can tell because when you find their slopes, one has a slope of -4/5, and the other has a slope of +5/4. Perpendicular lines have slopes that are "negative reciprocals" of each other, like these do.

(The slope of a linear equation in the form Ax +By = C is -A/B)

Answer 2

Hello,

I assume that you mean parallel - perpendicular or neither.

Put them in the form y = mx +b the slope-intercept form

4x + 5y = 2 subtract 4x from both sides giving us 5y = -4x + 2 now divide by 5 and we have y = -4/5 x + 2/5

Second one
5x - 4y = 1 subtract 5x from both sides giving us -4y = -5x + 1 now divide both sides by -4 and we have

y = 5/4x - 1/4
To be parallel the slopes (the m values) must be the same the first m = 5/4 and the second m = -4/5 the are not equal so the lines are not parallel.

To be perpendicular the slopes mus be opposite reciprocals now we have 5/4 and -4/5 they are oppostie reciprocals so the lines are perpendicular.

Hope This Helps!!!