Let's break down the problem step-by-step.
Problem Summary
- Julie needs to cut 4 pieces of yarn.
- Each piece has the same length , represented by xxx.
- There is also one piece of yarn that is 7 inches long.
- We want to write an equation for the total length of all the yarn she ends up cutting, represented by yyy.
- We also want to determine if the graph of this equation is continuous or discrete.
Step 1: Define the variables
- xxx = length of each of the 4 equal pieces of yarn (in inches)
- yyy = total length of all the yarn Julie cuts (in inches)
Step 2: Write the equation for total length yyy
- Julie cuts 4 pieces of length xxx, so total length from these pieces is 4x4x4x.
- She also has one piece that is 7 inches long.
- Total length yyy is the sum of these:
y=4x+7y=4x+7y=4x+7
Step 3: Discuss the graph of the equation
- The equation y=4x+7y=4x+7y=4x+7 is a linear equation.
- The graph of this equation is a straight line.
- Since xxx represents length, it can take any non-negative real value (assuming length can't be negative).
- Therefore, the graph is continuous over the domain x≥0x\geq 0x≥0.
Final answer:
{y=4x+7Graph is continuous for x≥0\boxed{ \begin{cases} y=4x+7\\ \text{Graph is continuous for }x\geq 0 \end{cases} }{y=4x+7Graph is continuous for x≥0
If you want, I can also help you plot the graph or explain more about continuous vs discrete graphs!
