Question

What is the parametric form of the linear equation 3x - 2y = 16

Answer 1

y=3x/2 -8

Answer 2

This is the slope-intercept form, I need the parametric form.

Answer 3

First you differentiate
3x - 2y = 16
\[3-2\frac{dy}{dx}=0\]
\[3/2=\frac{dy}{dx}\]

Answer 4

then you set \[\Huge \frac{\frac{dy}{dt}}{\frac{dx}{dt}}=\frac{3}{2}\]
\[\Huge \frac{\frac{dy}{dt}}{\frac{dx}{dt}}=\frac{(\frac{3}{2})}{1}\]
\[\frac{dy}{dt}=\frac{3}{2} ~\text{and}~ \frac{dx}{dt}=1\]
Then integrate both dy/dt and dx/dt
x=t+c , and y=3t/2 +d

Answer 5

ty!

Answer 6

Differentiation and integration? No need to make it so complicated...

3x - 2y = 16
3x = 16 + 2y
t = 3x, t = 16 + 2y

x = t/3, y = .5t - 8