Eliminate the parameter for the following set of parametric equations show your work
X = t + 6
Y = 3t - 1
x = t + 6
Subract 6 to both sides
x - 6 = t
t = x - 6
y = 3 t - 1
y = 3 ( x - 6 ) - 1
y = 3 x - 18 - 1
y = 3 x - 19
To eliminate the parameter, t, we need to express one variable, either x or y, solely in terms of the other variable. Let's do that step by step:
1. Start with the given parametric equations:
X = t + 6
Y = 3t - 1
2. Solve the first equation, X = t + 6, for t:
X - 6 = t
3. Substitute this expression for t into the second equation, Y = 3t - 1:
Y = 3(X - 6) - 1
4. Simplify the equation:
Y = 3X - 18 - 1
= 3X - 19
Therefore, by eliminating the parameter t, we obtain the equation Y = 3X - 19, which relates x and y without the need for the parameter.