Answer:
Answer in explanation.
Step-by-step explanation:
Lets take
[tex]y = \frac{3}{4} x - 5[/tex]
as L1.
Take L2 the line perpendicular to L1.
Standard form of equation of line:
y=mx+c, where m = slope and c = y-intercept.
Since L1 and L2 are perpendicular,
mL1 x mL2 = -1
Substitute mL1 into the equation,
3/4 x mL2 = -1
mL2 = -1 ÷ 3/4
mL2 = -4/3
L2 : y = mx+ c
Substitute y = 6, x = 8 and m = -4/3 into the equation,
[tex]6 = - \frac{4}{3} (8) + c \\ 6 = - \frac{32}{3} + c \\ c = 6 + \frac{32}{3} \\ = 16 \frac{2}{3} [/tex]
therefore L2:
[tex]y = - \frac{4}{3}x + 16 \frac{2}{3} [/tex]
Lets take L3 as the line parallel to L1.
Since L3 and L1 are parallel,
mL3 = mL1 = 3/4
equation of line: y = mx+c
substitute y = 6, x = 8 and m = 3/4 into equation.
[tex]6 = ( \frac{3}{4} )(8) + c \\ 6 = 6 + c \\ c = 6 - 6 \\ = 0[/tex]
therefore L3:
[tex]y = \frac{3}{4} x[/tex]
