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 the slope for mm gives:
6 = (color(red)(4) - color(blue)(10))/(color(red)(r) - color(blue)(8))6=4−10r−8
We can now solve for rr:
6 = (-6)/(color(red)(r) - color(blue)(8))6=−6r−8
(r - 8) * 6 = (r - 8) * (-6)/(color(red)(r) - color(blue)(8))(r−8)⋅6=(r−8)⋅−6r−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
