To find the location of the point on the number line that is [tex]\(\frac{2}{7}\)[/tex] of the way from [tex]\(A = 18\)[/tex] to [tex]\(B = 4\)[/tex], follow these steps:
1. Determine the difference between points [tex]\(A\)[/tex] and [tex]\(B\)[/tex]:
[tex]\[
B - A = 4 - 18 = -14
\][/tex]
2. Calculate [tex]\(\frac{2}{7}\)[/tex] of this difference:
[tex]\[
\frac{2}{7} \times (-14) = \frac{2 \times -14}{7} = \frac{-28}{7} = -4
\][/tex]
3. Add this value to point [tex]\(A\)[/tex] to find the location:
[tex]\[
A + \left(\frac{2}{7} \times (B - A)\right) = 18 + (-4) = 14
\][/tex]
Therefore, the location of the point that is [tex]\(\frac{2}{7}\)[/tex] of the way from [tex]\(A\)[/tex] to [tex]\(B\)[/tex] is [tex]\(\boxed{14}\)[/tex].
