Given this set of parametric equations, find the scalar equation:
x = 1 + 2t
y = 1 - 3t
t = (x-1)/2
y = 1 - 3(x-1)/2
To find the scalar equation for the given set of parametric equations, we need to eliminate the parameter 't' and express 'y' solely in terms of 'x'.
Given:
x = 1 + 2t
y = 1 - 3t
The first equation can be rearranged to solve for 't':
2t = x - 1
t = (x - 1) / 2
Next, substitute this expression for 't' in the second equation:
y = 1 - 3((x - 1) / 2)
y = 1 - (3/2)(x - 1)
y = 1 - (3/2)x + 3/2
Simplifying further:
y = (-3/2)x + 5/2
Therefore, the scalar equation that represents the given set of parametric equations is:
y = (-3/2)x + 5/2