Question

Find the slope-intercept form of the line given that x=-2+3t y=4-6t.

Answer 1

x=-2+3t , y=4-6t
solve each one for t

x = -2 + 3t
3t = x+2
t = (x+2)/3

in the same way:
t = (4-y)/6

then: (x+2)/3 = (4-y)/6
cross-multiply
6x + 12 = 12 - 3y

simplify and arrange into the form requested

Answer 2

m = Y/X = (4-6t)/(-2+3t) = -2(-2+3t)/(-2+3t) = -2.
Y = mx+b
4-6t = -2(-2+3t)+b
4-6t = 4-6t+b
b = 0.
Y = -2x+0
Y = -2x.