Write Parametric equations of -3x+1/2y=2
we know x =rcosØ and y = rsinØ
-3rcosØ + (1/2)rsinØ = 2
-6rcosØ + rsinØ = 2
r(sinØ - 6cosØ) = 2
or
r = 2/(sinØ - 6cosØ)
looks good:
http://www.wolframalpha.com/input/?i=polar+r+%3D+2%2F%28sinx+-+6cosx%29
Reiny gave you good polar coordinates, but if all you want is parametric equations, try
x = t/3
y = 1 + t/2
or
x = -(2+t)/3
y = -2t
To write the parametric equations of a line, we need to express x and y in terms of a parameter, usually denoted as t. However, before we can do that, let's rearrange the equation -3x + (1/2)y = 2 into slope-intercept form (y = mx + b).
-3x + (1/2)y = 2
First, we'll isolate y by adding 3x to both sides of the equation:
(1/2)y = 3x + 2
Next, we'll multiply both sides of the equation by 2 to eliminate the fraction:
2 * (1/2)y = 2 * (3x + 2)
y = 6x + 4
Now that we have the equation in slope-intercept form, we can proceed to write the parametric equations.
For the x-parameter, we can define it as t, which means x = t.
For the y-parameter, we can substitute y with 6x + 4:
y = 6(t) + 4
Therefore, the parametric equations for the line -3x + (1/2)y = 2 are:
x = t
y = 6t + 4