Consider the line passing through the points (2, 1) and (-2, 3). Find the parametric equation for y if x = t + 1.

See:

http://www.jiskha.com/display.cgi?id=1304191154

To find the parametric equation for y, we first need to find the slope of the line passing through the given points. The slope of a line can be found using the formula:

m = (y2 - y1) / (x2 - x1)

Using the points (2, 1) and (-2, 3) from the given information:

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

Now that we have the slope, we can use it to write the equation of the line in point-slope form. The point-slope form of a line is given by:

y - y1 = m(x - x1)

Using the point (2, 1) as the base point:

y - 1 = (-1/2)(x - 2)

Next, we can simplify the equation:

y - 1 = (-1/2)(x) - (-1/2)(2)
y - 1 = (-1/2)x + 1/2

Finally, we can rewrite the equation in the desired parametric form. Since x = t + 1, we can substitute this value into the equation:

y - 1 = (-1/2)(t + 1) + 1/2
y - 1 = (-1/2)t - 1/2 + 1/2
y - 1 = (-1/2)t

Thus, the parametric equation for y is y = (-1/2)t + 1.