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.