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Julie needs to cut 4 pieces of yarn, each with the same length, and a piece of yarn 7.75 inches long. Let [tex] x [/tex] represent the length of each of the equal pieces of yarn that Julie decides to cut.

What is the equation that can be used to determine the total length of all of the yarn that she ends up cutting, [tex] y [/tex]? Is the graph of the equation continuous or discrete?

A. [tex] y = 7.75 x + 4 [/tex]; discrete
B. [tex] y = 7.75 x + 4 [/tex]; continuous
C. [tex] y = 4 x + 7.75 [/tex]; discrete
D. [tex] y = 4 x + 7.75 [/tex]; continuous



Answer :

GinnyAnswer
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]

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