Find a set of parametric equations for y=5x+11 given the parameter t=2-x show your work
To find a set of parametric equations for the equation y = 5x + 11 given the parameter t = 2 - x, we can follow these steps:
Step 1: Let's start by solving the given parameter equation t = 2 - x for x.
t = 2 - x
Subtract 2 from both sides:
t - 2 = -x
Multiply both sides by -1:
-t + 2 = x
Step 2: Now that we have x in terms of t, substitute this value into the original equation y = 5x + 11.
y = 5(-t + 2) + 11
Distribute the 5:
y = -5t + 10 + 11
Simplify:
y = -5t + 21
Therefore, the set of parametric equations for y = 5x + 11 given the parameter t = 2 - x is:
x = -t + 2
y = -5t + 21
These parametric equations represent the same line as the original equation y = 5x + 11, but expressed in terms of the parameter t.