Let's find the point that is [tex]\(\frac{1}{5}\)[/tex] of the way from the point [tex]\(-7\)[/tex] to the point [tex]\(17\)[/tex].
### Step-by-Step Solution:
1. Determine the distance between the two points:
We need to calculate the distance between [tex]\(-7\)[/tex] and [tex]\(17\)[/tex]:
[tex]\[ \text{Distance} = 17 - (-7) = 17 + 7 = 24 \][/tex]
So, the total distance is [tex]\(24\)[/tex].
2. Calculate [tex]\(\frac{1}{5}\)[/tex] of the distance:
Next, we find [tex]\(\frac{1}{5}\)[/tex] of the distance:
[tex]\[ \frac{1}{5} \text{ of } 24 = \frac{24}{5} = 4.8 \][/tex]
3. Move [tex]\(\frac{1}{5}\)[/tex] of the distance from point [tex]\(-7\)[/tex]:
Since [tex]\(-7\)[/tex] is our starting point, we add [tex]\(4.8\)[/tex] to [tex]\(-7\)[/tex] to find the required point:
[tex]\[ \text{Point} = -7 + 4.8 = -2.2 \][/tex]
Therefore, [tex]\(\frac{1}{5}\)[/tex] of the way from [tex]\(-7\)[/tex] to [tex]\(17\)[/tex] is [tex]\(-2.2\)[/tex].
The answer is
[tex]\[ \boxed{-2.2} \][/tex]
