Let's carefully analyze what needs to be done to find the total length of yarn Julie cuts.
1. Define the lengths involved:
- Let [tex]\( x \)[/tex] represent the length of each of the 4 equal pieces of yarn.
- There is an additional piece of yarn that has a fixed length of 7.75 inches.
2. Formulate the total length:
- The total length [tex]\( y \)[/tex] is comprised of the sum of lengths of the 4 equal pieces and the one additional piece.
- The total length of the 4 equal pieces would be [tex]\( 4x \)[/tex].
3. Combine the lengths into an equation:
- Add the length of the 4 equal pieces and the additional piece: [tex]\( y = 4x + 7.75 \)[/tex].
So, the equation to determine the total length of all the yarn Julie ends up cutting is:
[tex]\[ y = 4x + 7.75 \][/tex]
Next, we need to determine the nature of the graph:
- The variable [tex]\( x \)[/tex] can take any positive real number value since [tex]\( x \)[/tex] represents a length, and lengths can vary continuously in the real world.
- Therefore, the graph of the equation [tex]\( y = 4x + 7.75 \)[/tex] is continuous because there are no restrictions on the possible values of [tex]\( x \)[/tex] other than being positive.
Hence, the correct equation and the nature of its graph is:
[tex]\[ y = 4x + 7.75; \text{continuous} \][/tex]
