The line through ( − 9 , 3 ) and ( 6 , − 7 ) also goes through the point ( t , − 2 ) for

Question

The line through  and  also goes through the point  for T=

Answer 1

(-7 - 3) / (6 + 9) = (-2 - 3) / (t + 6)

Can you solve for t and answer?

Answer 2

first find the slope: (3-[-7])/(-9-6)=10/-15=-2/3, m=-2/3

now use y=mx+b to find the equation of the line going through points (-9,3) and (6,-7) or use the point-slope form

using the point-slope form: y-y(1)=m(x-x[1])

pick one of the points, say (-9,3)

y-3=(-2/3)(x-[-9])

y-3=(-2/3)x-(-2/3)(-9)

y-3=(-2/3)x-6

y=(-2/3)x-3

now use the point (t,-2) where t will be "x"

-2=(-2/3)x-3

(-2/3)x=1

x=(-3/2), so t=-3/2

Answer 3