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

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

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.

To find the slope-intercept form of the line, we need to express the equation in the form y = mx + b, where m is the slope of the line, and b is the y-intercept.

Given the parametric equations:
x = -2 + 3t
y = 4 - 6t

We first need to isolate t in terms of x and y. Let's start with the x equation:
x = -2 + 3t

Adding 2 to both sides:
x + 2 = 3t

Dividing by 3:
(x + 2) / 3 = t

Now, let's substitute this value of t into the y equation:
y = 4 - 6t

Replacing t:
y = 4 - 6((x + 2) / 3)

Simplifying:
y = 4 - 2(x + 2)
y = 4 - 2x - 4

Combining like terms:
y = -2x

Therefore, the slope-intercept form of the line is y = -2x, where the slope (m) is -2 and the y-intercept (b) is 0.