Final answer:
The complete equation of the line through the points (2,-2) and (4,1) is y = (3/2)x - 5, calculated using the slope derived from the two points and the point-slope form of the equation of a line.
Step-by-step explanation:
To complete the equation of the line through the points (2,-2) and (4,1), we must first calculate the slope (m) of the line. The slope is given by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are our given points. Thus:
m = (1 - (-2)) / (4 - 2) = 3 / 2
Now that we have the slope, we use the point-slope form of a line equation, which is y - y1 = m(x - x1). Using either of the given points, let's use (2, -2) to construct the equation:
y - (-2) = 3/2(x - 2)
Simplifying, we get:
y + 2 = 3/2(x - 2)
y = (3/2)x - 3 - 2
y = (3/2)x - 5
Therefore, the complete equation of the line is y = (3/2)x - 5.