To find the equation of the line that passes through the points (4, -2) and (-1, 3), we can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
where m is the slope of the line, and (x1, y1) is one of the given points.
First, we can find the slope of the line using the two points:
m = (y2 - y1) / (x2 - x1)
m = (3 - (-2)) / (-1 - 4)
m = 5 / (-5)
m = -1
Next, we can choose one of the points to plug into the point-slope form. Let's choose the point (4, -2):
y - (-2) = -1(x - 4)
Simplifying this equation, we get:
y + 2 = -x + 4
Subtracting 2 from both sides, we get:
y = -x + 2
Therefore, the equation of the line that passes through the points (4, -2) and (-1, 3) is y = -x + 2.