To find the point on the number line that is [tex]\(\frac{3}{5}\)[/tex] of the way from [tex]\(A = 2\)[/tex] to [tex]\(B = 17\)[/tex], follow these steps:
1. Calculate the difference between [tex]\(B\)[/tex] and [tex]\(A\)[/tex]:
[tex]\[
B - A = 17 - 2 = 15
\][/tex]
2. Determine the fraction of the way from [tex]\(A\)[/tex] to [tex]\(B\)[/tex]:
Since we need [tex]\(\frac{3}{5}\)[/tex] of the way, we multiply the difference by [tex]\(\frac{3}{5}\)[/tex].
[tex]\[
\text{Position from } A = 15 \times \frac{3}{5} = 15 \times 0.6 = 9
\][/tex]
3. Calculate the actual position on the number line:
To find the exact point, add the calculated position from [tex]\(A\)[/tex] to [tex]\(A\)[/tex] itself:
[tex]\[
\text{Position on line} = A + 9 = 2 + 9 = 11
\][/tex]
Hence, the location of the point on the number line that is [tex]\(\frac{3}{5}\)[/tex] of the way from [tex]\(A = 2\)[/tex] to [tex]\(B = 17\)[/tex] is [tex]\(\boxed{11}\)[/tex].
