In: Math
For the following exercises, rewrite the parametric equation as a Cartesian equation by building an x-y table.
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.
Therefore, the Cartesian form of above parametric equations is 3x + y = 14.