Question

julie needs to cut 4 pieces of yarn, each with the same length, and a piece of yarn 7.75 inches long. let x 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, y? is the graph of the equation continuous or discrete?
○ y=7.75x+4; discrete
○ y=7.75x+4; continuous
○ y=4x+7.75; discrete
○ y=4x+7.75; continuous

Explanation:

Step1: Determine the equation

Julie cuts 4 pieces of length \( x \), so their total length is \( 4x \). She also cuts a piece of 7.75 inches. So the total length \( y \) is \( y = 4x + 7.75 \).

Step2: Determine if graph is continuous or discrete

The length of yarn can be any real number (e.g., 1.5 inches, 2.3 inches, etc.), so the variable \( x \) can take any real - valued input. A function with a domain of all real numbers (or a subset of real numbers where values are not restricted to distinct, separate values) has a continuous graph. Also, the equation \( y = 4x+7.75 \) is a linear equation, and linear equations (except for those with restricted domains that make them discrete) have continuous graphs. Since the length of yarn can be any positive real number (as length can be measured in fractions of an inch), the graph of \( y = 4x + 7.75 \) (where \( x>0 \)) is continuous.

Answer:

\( y = 4x + 7.75 \); continuous (the option: \( y = 4x+7.75 \); continuous)