Write the equation of a line that is perpendicular to the given line and that passes through the given point. y-4=5/2(x+3); (-3,4)

Y - 4 = 5/2(x + 3)slope here is 5/2. A perpendicular line will have a negative reciprocal slope. All that means is " flip " the slope and change the sign. So our perpendicular line will have a slope of -2/5 (see how I flipped the slope and changed the sign)

I am not sure what form u need this in...so I will write a few...

point-slope form :
y - y1 = m(x - x1)
slope(m) = -2/5
(-3,4)x1 = -3 and y1 = 4
now we sub
y - 4 = -2/5(x - (-3) =
y - 4 = -2/5(x + 3) <== point slope form

y - 4 = -2/5(x + 3)
y = -2/5x - 6/5 + 4
y = -2/5x - 6/5 + 20/5
y = -2/5x + 14/5 <== slope intercept form

y = -2/5x + 14/5
2/5x + y = 14/5...multiply by 5
2x + 5y = 14 <== standard form