Answer
a.$24y-40x+9=0$
b. $40y+24x-53=0$
Work Step by Step
Put the equation into slope-intercept form.
$5x-3y=0$
$3y=5x$
$y=\frac{5}{3}x$
The slope is $\frac{5}{3}$.
a. Parallel lines have the same slope.
$y=mx+b$
$y=\frac{5}{3}x+b$
Plug in $(\frac{3}{4}, \frac{7}{8})$ to find b.
$\frac{7}{8}=\frac{5}{3}(\frac{3}{4})+b$
$\frac{7}{8}=\frac{5}{4}+b$
$\frac{7}{8}=\frac{10}{8}+b$
$b=-\frac{3}{8}$
$y=\frac{5}{3}x-\frac{3}{8}$
$y-\frac{5}{3}x+\frac{3}{8}$
Multiply both sides by 24.
$24y-40x+9=0$
b. The slope of a perpendicular line is the negative reciprocal of the original slope, so the slope for this line is $-\frac{3}{5}$.
$y=-\frac{3}{5}x+b$
Plug in $(\frac{3}{4}, \frac{7}{8})$ to find b.
$\frac{7}{8}=-\frac{3}{5}*\frac{3}{4}+b$
$\frac{7}{8}=-\frac{9}{20}+b$
$\frac{70}{80}=-\frac{36}{80}+b$
$\frac{106}{80}=b$
$b=\frac{53}{40}$
$y=-\frac{3}{5}x+\frac{53}{40}$
$y+\frac{3}{5}x-\frac{53}{40}$
Multiply both sides by 40.
$40y+24x-53=0$
