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 points in the problem and solving for pp gives:
3 = (color(red)(p) - color(blue)(-4))/(color(red)(0) - color(blue)(-2))3=p−−40−−2
3 = (color(red)(p) + color(blue)(4))/(color(red)(0) + color(blue)(2))3=p+40+2
3 = (p + 4)/23=p+42
color(red)(2) * 3 = color(red)(2) * (p + 4)/22⋅3=2⋅p+42
6 = cancel(color(red)(2)) * (p + 4)/color(red)(cancel(color(black)(2)))
6 = p + 4
6 - color(red)(4) = p + 4 - color(red)(4)
2 = p + 0
2 = p
p = 2
