Write an equation of the line perpendicular to y=2/5x+3 and through (4,-4)

Y = 2/5x + 3. The slope here is 2/5. A perpendicular line will have a negative reciprocal slope. To find the negative reciprocal. we " flip " the slope and change the sign. So the perpendicular line will need a slope of -5/2.

y = mx + b
slope(m) = -5/2
(4,-4)x = 4 and y = -4
now we sub and find b, the y int
-4 = -5/2(4) + b
-4 = - 10 + b
-4 + 10 = b
6 = b

so ur perpendicular line is : y = -5/2x + 6