How do you find the value of r such the points (8,10), (r,4) with slope m=6?

Question

Abigail Allen · Accepted Answer

See the entire solution process below:

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#

Eva Adamson · Answer

undefined To find the value of $ r $ such that the points $ (8,10) $ and $ (r,4) $ have a slope of $ m = 6 $, you can use the slope formula:

$$ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} $$

Substitute the given points and slope into the formula, then solve for $ r $.