   Chapter 10.1, Problem 6E

Chapter
Section
Textbook Problem

# (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. (b) Eliminate the parameter to find a Cartesian equation of the curve. 6. x = 3t + 2, y = 2t + 3

(a)

To determine

To plot: The curve using the parametric equations. x=3t+2 and y=2t+3 .

Explanation

Given data:

The parametric equation for the variable x is as follows.

x=3t+2 (1)

The parametric equation for the variable y is as follows.

y=2t+3 (2)

Calculation:

The value of t is increased from 4 to 4 with a step value of 1 and substituted in the parametric Equations (1) and (2) to obtain the value of x and y respectively.

Substitute 4 for t in Equation (1).

x=3t+2=3(4)+2=12+2x=10

Substitute 4 for t in Equation (2).

y=2t+3=2(4)+3=8+3y=5

The values of x and y for each step value of t is tabulated in the below table

(b)

To determine

To find: obtain a Cartesian equation of the curve by eliminating parameter t .

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