21. 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); (-7,8)

In y - y1 = m(x - x1) form, the slope will be in the m position. So in ur equation, which is in that form, the number in the m position (the slope) is 5/2. A perpendicular line will have a negative reciprocal slope. To find the negative reciprocal, u flip the original slope and change the sign. So with our slope of 5/2we flip it making it 2/5we change the sign making it -2/5. So our perpendicular line will have a slope of -2/5.

y = mx + b
slope(m) = -2/5
(-7,8)x = -7 and y = 8
now we sub into the formula and find b, the y int
8 = -2/5(-7) + b
8 = 14/5 + b
8 - 14/5 = b
40/5 - 14/5 = b
26/5 = b
so ur perpendicular equation is : y = -2/5x + 26/5 <==