Question 360818
Find a real number, n , such that the line containing the points (-6,3)
 and (-2,6) contains the point (n,5)
;
Find the slope of the given points, where:
x1=-6; y1=3
x2=-2; y2=6
:
slope m = {{{(y2-y1)/(x2-x1)}}}
:
m = {{{(6-3)/(-2-(-6))}}} = {{{3/4}}}
:
Find the equation using the point/slope form
y - 3 = {{{3/4}}}(x - (-6))
y - 3 = {{{3/4}}}(x + 6)
y - 3 = {{{3/4}}}x + 4.5
y = {{{3/4}}}x + 4.5 + 3
y = {{{3/4}}}x + 7.5
or
y = .75x + 7.5
:
Find n, 
.75n + 7.5 = 5
.75n = 5 - 7.5
.75n = -2.5
n = {{{-2.5/.75}}}
n = -3{{{1/3}}} when y = 5