How do you find the missing #y# values for a line with a slope of #-10# which goes through #(2, 8)# and #(3, s)#?

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Answer 1 · 2017-06-11T19:04:05

See a 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 slope and values from the points in the problem gives:

#-10 = (color(red)(8) - color(blue)(s))/(color(red)(2) - color(blue)(3))#

We can now solve for #s#:

#-10 = (color(red)(8) - color(blue)(s))/-1#

#-10 = -(color(red)(8) - color(blue)(s))/1#

#-10 = -(color(red)(8) - color(blue)(s))#

#-10 = -color(red)(8) + color(blue)(s)#

#8 - 10 = 8 - color(red)(8) + color(blue)(s)#

#-2 = 0 + color(blue)(s)#

#-2 = color(blue)(s)#

#color(blue)(s) = -2#