Alright, let's break down the given information to provide the detailed answers for the boxes.
1. Finding the y-intercept of [tex]\(\overleftrightarrow{A B}\)[/tex]:
The coordinates of points [tex]\(A\)[/tex] and [tex]\(B\)[/tex] are [tex]\((14, -1)\)[/tex] and [tex]\((2, 1)\)[/tex], respectively. The y-intercept ([tex]\(b\)[/tex]) of line [tex]\(\overleftrightarrow{A B}\)[/tex] is [tex]\( 1.333 \)[/tex].
2. Finding the equation of [tex]\(\overleftrightarrow{A B}\)[/tex]:
The slope ([tex]\(m\)[/tex]) of the line passing through points [tex]\(A\)[/tex] and [tex]\(B\)[/tex] is [tex]\( -0.167 \)[/tex]. Therefore, the equation of the line [tex]\(\overleftrightarrow{A B}\)[/tex] (which is also the same line as [tex]\(\overleftrightarrow{B C}\)[/tex]) is given by [tex]\( y = mx + b \)[/tex]. Substituting the calculated values, the equation is [tex]\( y = -0.167x + 1.333 \)[/tex].
3. Finding the x-coordinate of point [tex]\(C\)[/tex]:
Given the y-coordinate of point [tex]\(C\)[/tex] is 13, we need to find the corresponding x-coordinate on the line [tex]\(\overleftrightarrow{A B}\)[/tex] (i.e., [tex]\( y = -0.167x + 1.333 \)[/tex]). The calculated x-coordinate is [tex]\( -70 \)[/tex].
Putting these into the correct answers for the boxes:
The [tex]$y$[/tex]-intercept of [tex]\(\overleftrightarrow{A B}\)[/tex] is [tex]\(\boxed{1.333}\)[/tex] and the equation of [tex]\(\overleftrightarrow{A B}\)[/tex] is [tex]\(y = \boxed{-0.167}x + \boxed{1.333}\)[/tex]. If the y-coordinate of point [tex]\(C\)[/tex] is [tex]\(13\)[/tex], its x-coordinate is [tex]\(\boxed{-70}\)[/tex].
