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Consider the parametric equations below. x = 5t - 3 y = 4t + 3 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases. (Do this on paper. Your instructor may ask you to turn in this work.) (b) Eliminate the parameter to find a Cartesian equation of the curve. y

Answer :

Answer:

(a)

You plug in "t" in each of the equations.

(b)

y = 4(x+3)/5  + 3  = 4/5 x  + 12/5 + 3 = 4/5 x + 27/5

Step-by-step explanation:

(a)

For this part what you do is plug in "t" in each of the equations.

For example, let  t=1 , then

x = 5(1) - 3 = 2

y = 4(1) + 3 = 7

then, you graph the point (2,7) in the plane.

For example,  t = 2 , then

x = 5(2) - 3  = 7

y = 4(2) + 3  = 11

Then you graph the point (7,11) in the plane.

(b)

Notice that

x = 5t -3

x+3 = 5t  

(x+3) /5  =   t

We replace that in the equation for "y" and get

y = 4(x+3)/5  + 3  = 4/5 x  + 12/5 + 3 = 4/5 x + 27/5

and that is an equation cartesian equation. Which solves the problem.  

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