We have been given parametric equations [tex]x=2t[/tex] and [tex]y=1-t[/tex]. We are asked to write the equation of line with the given parametric equations in slope intercept form.
First of all, we will solve for t from 1st equation as:
[tex]\frac{x}{2}=\frac{2t}{2}[/tex]
[tex]\frac{x}{2}=t[/tex]
[tex]t=\frac{x}{2}[/tex]
Now we will substitute this value in 2nd equation.
[tex]y=1-\frac{x}{2}[/tex]
[tex]y=-\frac{1}{2}x+1[/tex]
Therefore, our required equation would be [tex]y=-\frac{1}{2}x+1[/tex] and option 'a' is the correct choice.
