First, we need to determine the slope. The slope can be found by using the formula: m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))
Where m is the slope and (color(blue)(x_1, y_1)) and (color(red)(x_2, y_2)) are the two points on the line.
Substituting the values from the points in the problem gives:
m = (color(red)(-3) - color(blue)(3))/(color(red)(-2) - color(blue)(-8)) = (color(red)(-3) - color(blue)(3))/(color(red)(-2) + color(blue)(8)) = (-6)/6 = -1
Now, we can use the point-slope formula to find the equation for the line through these points. The point-slope formula states: (y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))
Where color(blue)(m) is the slope and color(red)(((x_1, y_1))) is a point the line passes through.
Substituting the slope we calculated and the first point gives:
(y - color(red)(3)) = color(blue)(-1)(x - color(red)(-8))
(y - color(red)(3)) = color(blue)(-1)(x + color(red)(8))
Or, we can substitute the slope we calculated and the second point giving:
(y - color(red)(-3)) = color(blue)(-1)(x - color(red)(-2))
(y + color(red)(3)) = color(blue)(-1)(x + color(red)(2))
