To write the equation in point-slope form, we can use the formula:
y - y1 = m(x - x1)
where (x1, y1) are the coordinates of one point on the line, and m is the slope of the line.
First, let's find the slope using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (1, -2) and (x2, y2) = (-1, 8).
Plugging in the values, we have:
m = (8 - (-2)) / (-1 - 1)
m = 10 / -2
m = -5
Now that we have the slope, we can choose any of the given points and substitute the values into the point-slope form equation.
Let's choose the point (1, -2).
Substituting the values into the equation:
y - (-2) = -5(x - 1)
Simplifying the equation:
y + 2 = -5x + 5
Now, we can rearrange the equation to isolate y:
y = -5x + 3
Therefore, the equation in point-slope form of the line that passes through the points (1, -2) and (-1, 8) is y = -5x + 3.