First, 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))m=y2−y1x2−x1
Where mm is the slope and (color(blue)(x_1, y_1)x1,y1) and (color(red)(x_2, y_2)x2,y2) are the two points on the line.
Substituting the values from the problem gives:
m = (color(red)(3) - color(blue)(-3))/(color(red)(2) - color(blue)(4))m=3−−32−4
m = (color(red)(3) + color(blue)(3))/(color(red)(2) - color(blue)(4))m=3+32−4
m = 6/-2m=6−2
m = -3m=−3
The point-slope formula states: (y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))(y−y1)=m(x−x1)
Where color(blue)(m)m is the slope and color(red)(((x_1, y_1))) is a point the line passes through.
Substituting the values from one of the points in the problem and the slope we calculated gives:
(y - color(red)(-3)) = color(blue)(-3)(x - color(red)(4))
(y + color(red)(3)) = color(blue)(-3)(x - color(red)(4))
Substituting the values from one the other points in the problem and the slope we calculated gives:
(y - color(red)(3)) = color(blue)(-3)(x - color(red)(2))
