Final answer:
The equation of the line that goes through the points (-2, 1) and (1, -1) is y = (-2/3)x + (4/3).
Step-by-step explanation:
To determine the equation of a line that goes through two points, we can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
Where (x1, y1) are the coordinates of one point, and m is the slope of the line.
Using the points (-2, 1) and (1, -1), we can calculate the slope using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the values, we have:
m = (-1 - 1) / (1 - (-2)) = -2/3
So, the equation of the line is y - 1 = (-2/3)(x - (-2)), which simplifies to y - 1 = (-2/3)(x + 2) or y = (-2/3)x + (4/3).