Certainly! Let's approach this problem step-by-step.
1. Identify the two points on the number line:
- The first point, [tex]\( \text{point1} \)[/tex], is [tex]\(-7\)[/tex].
- The second point, [tex]\( \text{point2} \)[/tex], is [tex]\(17\)[/tex].
2. Find the distance between the two points:
[tex]\[
\text{Distance} = \text{point2} - \text{point1} = 17 - (-7) = 17 + 7 = 24
\][/tex]
So, the distance between the points [tex]\(-7\)[/tex] and [tex]\(17\)[/tex] is [tex]\(24\)[/tex].
3. Calculate the fraction of the way:
We need to determine the point that is [tex]\(\frac{2}{5}\)[/tex] of the way from [tex]\(-7\)[/tex] to [tex]\(17\)[/tex].
4. Calculate the actual distance corresponding to this fraction:
[tex]\[
\text{Fractional distance} = \text{Distance} \times \frac{2}{5} = 24 \times \frac{2}{5} = 24 \times 0.4 = 9.6
\][/tex]
5. Find the coordinate of the point [tex]\(\frac{2}{5}\)[/tex] of the way from [tex]\(-7\)[/tex] to [tex]\(17\)[/tex]:
Start from [tex]\(-7\)[/tex] and move [tex]\(9.6\)[/tex] units towards [tex]\(17\)[/tex].
[tex]\[
\text{Point} = \text{point1} + \text{Fractional distance} = -7 + 9.6 = 2.6
\][/tex]
Therefore, the point on the number line that is [tex]\(\frac{2}{5}\)[/tex] of the way from [tex]\(-7\)[/tex] to [tex]\(17\)[/tex] is [tex]\(2.6\)[/tex].
So, the correct answer is [tex]\(2.6\)[/tex].
