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 the slope for #m# gives:
#6 = (color(red)(4) - color(blue)(10))/(color(red)(r) - color(blue)(8))#
We can now solve for #r#:
#6 = (-6)/(color(red)(r) - color(blue)(8))#
#(r - 8) * 6 = (r - 8) * (-6)/(color(red)(r) - color(blue)(8))#
#6r - 48 = cancel((r - 8)) * (-6)/cancel(color(red)(r) - color(blue)(8))#
#6r - 48 = -6#
#6r - 48 + color(red)(48) = -6 + color(red)(48)#
#6r - 0 = 42#
#6r = 42#
#(6r)/color(red)(6) = 42/color(red)(6)#
#(color(red)(cancel(color(black)(6)))r)/cancel(color(red)(6)) = 7#
#r = 7#
