Question

21. Write the equation of a line that is perpendicular to the given line and that passes through the given point.

y - 3 = 8/3(x + 2); (-2, 3)

Answer 1

What is the given line?

Answer 2

y-3=8/3(x+2) is the line given
y=(8x+16)/3 +3
y=8/3x + 16/3+9/3
y=8/3x+25/3

perpendicular has the opposite slope. i.e. m1.m2=-1
if our slope(m1) is 8/3, the 8/3.m2=-1 or 8.m2=-3, m2=-3/8.
check: m1.m2=-1, 8/3 x -3/8 = -24/24 = -1 correct.

so the new slope will be -3/8
using our equation y-y1=m(x-x1) and our point (-2,3) we find the new line:
y-3=-3/8(x-[-2])
y-3=-3(x+2)/8
y=-3x/8-6/8
simplify: y=(-3x-6)/8
thats your answer

Answer 3

thank you that helps