Which is an equation of a line perpendicular to the line with the equation 5x-4y=8

y = (-4/5)x - 2

Step-by-step explanation:

Isolate the variable y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. First, subtract 5x from both sides:

5x - 4y = 8

5x (-5x) - 4y = 8 (-5x)

-4y = 8 - 5x

Isolate the variable y. Divide -4 from both sides.

(-4y)/-4 = (-5x + 8)/-4

y = (-5x + 8)/-4

y = (5/4)x - 2

The slope intercept form of the given line is: y = 5/4x - 2, with 5/4 being the slope.

To find the slope of the perpendicular line, you must find the opposite reciprocal of the slope.

The perpendicular line is the reciprocal (flip of the fraction) and opposite (change the sign) of the first line's slope (5/4), which means that it is -4/5

-4/5 is your perpendicular line's slope. Plug it into the slope-intercept form equation:

y = mx - 2

y = (-4/5)x - 2

Check to see if they are perpendicular by graphing.  See attached picture.

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