Question

How do you find the parametric equation for y if `x = e^t` for the line passing through the points (2,1) and (-2,3)?

Answer 1

Start with the slope-intercept form of the equation of a line. Use the two points to compute the slope and intercept. Substitute `e^t` for x.

Explanation:

The slope-intercept form of the equation of a line is:

`y = mx + b" [1]"`

Use the two points to compute the slope:

`m = (3 - 1)/(-2 - 2) = 2/-4 = -1/2`

Substitute `-1/2` for m into equation [1]:

`y = -1/2x + b" [2]"`

Substitute 2 for x, 1 for y, and then solve for b:

`1 = -1/2(2) + b`

`b = 2`

Substitute 2 for b into equation [2]:

`y = -1/2x + 2" [3]"`

Substitute `e^t` for x into equation [3]:

`y = -1/2e^t + 2" [4]"`

Equation [4] is the parametric equation for y.