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 and solving for #p# gives:
#3 = (color(red)(p) - color(blue)(-4))/(color(red)(0) - color(blue)(-2))#
#3 = (color(red)(p) + color(blue)(4))/(color(red)(0) + color(blue)(2))#
#3 = (p + 4)/2#
#color(red)(2) * 3 = color(red)(2) * (p + 4)/2#
#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#
