Certainly! Let's break down the problem step-by-step to find the correct equation and determine if the graph is continuous or discrete.
1. Understanding the Variables and Constants:
- Let [tex]\( x \)[/tex] represent the length of each of the 4 equal pieces of yam that Julie is cutting.
- The length of the yarn is given as 7.75 inches.
- [tex]\( y \)[/tex] is the total length of all the yam pieces combined.
2. Formulating the Equation:
- Julie cuts 4 pieces of yam, each with the same length [tex]\( x \)[/tex].
- Therefore, the total length of the 4 pieces of yam is [tex]\( 4 \times x \)[/tex].
- Adding the length of the yarn (7.75 inches), the total length [tex]\( y \)[/tex] can be expressed as:
[tex]\[
y = 4 \times x + 7.75
\][/tex]
3. Identifying Continuity:
- In this context, [tex]\( x \)[/tex] can be any non-negative real number because lengths can vary continuously.
- Therefore, the equation [tex]\( y = 4 x + 7.75 \)[/tex] charts a continuous relationship between [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
Given these explanations, the correct answer is:
[tex]\[ y = 4 x + 7.75; \text{ continuous } \][/tex]
