Question 218281
Write an equation in slope-intercept form of the line with parametric equations: x=2+3t and y=4+t


Step 1.  The slope-intercept form is given as y=mx+b with m as the slope and b is the y-intercept at x=0 or at point(0,b).


Step 2.  Given {{{y=4+t}}} or {{{t=y-4}}}.  Take this expression for and substitute it in {{{x=2+3t=2+3(y-4)}}}, then 


{{{x=2+3(y-4)}}}


{{{x=3y-10}}}


Add 10 to both sides of the equation


{{{x+10=3y-10+10}}}


{{{x+10=3y}}


Divide 3 to both sides of the equation


{{{x/3+10/3=3y/3}}}


{{{y=x/3+10/3}}}


Step 3.  ANSWER:  The equation is {{{y=x/3+10/3}}}


I hope the above steps were helpful.


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And good luck in your studies!


Respectfully,
Dr J