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)?

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Answer 1 · 2017-01-05T19:25:08

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.

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.