Question

Find the equation of the line that passes through the point (2,3) and is perpendicular to the line with the equation 3x + 4y ? 8 = 0. (b) what is the slope of that line? (c) what is the y-intercept? (d) sketch the line.

Answer 1

I'm assuming that ? is  a minus sign
3x+4y-8=0


a.
perpendicular lines have slopes that multiply to -1
ok
for ax+by-c=0
the slope is -a/b
so
3x+4y-8=0
slope=-3/4

perpendicular lines have slopes that multiply to get -1
-3/4 times what=-1
times both sides by -4/3
what=4/3

the slope is 4/3

y=mx+b
m=slope
b=y intercept

y=4/3x+b
we are given the point (2,3)
x=2 and y=3
3=4/3(2)+b
3=8/3+b
3-8/3=b
9/3-8/3=b
1/3=b

y=4/3x+1/3 is the equation



b. the slope is 4/3

c. the y intercept is 1/3


d. see attachment