Question

How do you find parametric equation for given curve: Line of slope 8 through (-4,9)?

Answer 1

`x = t , y = 8*t + 41`

Explanation:

A “parametric equation” is just a calculus term to say that you have an equation in terms of “parameters”, instead of the original variables. Using the standard line slope-intercept formula we calculate the intercept for this particular set of terms.
`y = m*x + b ; 9 = 8*(-4) + b ; 9 = -32 + b ; 32 + 9 = b ; b = 41`
The final linear equation is:
`y = 8*x + 41` To make it parametric we use
The graph of any function can be parameterized. For, if y = f(x) then let t = x so that x = t,   y = f(t).

`t = x , y = 8*t + 41`
http://colalg.math.csusb.edu/~devel/precalcdemo/param/src/param.html