Final answer:
The equation of the line that passes through the points (4,-2) and (-1,3) is y = -x+2.
Step-by-step explanation:
The equation of the line that passes through the points (4,-2) and (-1,3) can be found using the formula for the slope-intercept form of a line.
First, calculate the slope using the formula (y2-y1)/(x2-x1), where (x1,y1) and (x2,y2) are the coordinates of the two points.
In this case, the slope is (3-(-2))/(-1-4) = 5/(-5) = -1.
Then, use the point-slope form of the line, y-y1 = m(x-x1), where m is the slope and (x1,y1) is one of the points. Substituting the values, we get y-(-2) = -1(x-4), which simplifies to y+2 = -x+4.
Rearranging the equation, we get the equation of the line as y = -x+2.