For the following exercises, rewrite the parametric equation as a Cartesian equation by building an x-y table.

Expert Solution

Consider a set of parametric equations as follows,

x(t) = 4 - t ...... (1)

y(t) = 3t + 2 ...... (2)

t	x(t) = 4 - t	y(t) = 3t + 2
0	4 – 0 = 4	3 × 0 + 2 = 2
1	4 – 1 = 3	3 × 1 + 2 = 5
2	4 – 2 = 2	3 × 2 + 2 = 8
3	4 – 3 = 1	3 × 3 + 2 = 11
4	4 – 4 = 0	3 × 4 + 2 = 14

From the table, for 1 unit decrease in x, the variable y increases by 3 units. Hence, above equation is a linear equation with slope

m = change in y/change in x

= 3/(-1)

= -3

Since, the slope-point form of a straight line,

y – y1 = m(x – x1) ...... (3)

Substitute m = -3 and (x1, y1) = (4, 2), the Cartesian equation of above line will be,

y – 2 = (-3)[x – 4]

y – 2 = -3x + 12

3x + y = 14

Therefore, the Cartesian form of above parametric equations is 3x + y = 14.

Junaid answered 1 year ago

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