Let's go through the problem step-by-step to formulate our solution.
1. Identify Initial Length and Daily Consumption:
- Diep buys a loaf of bread that is initially 65 centimeters long.
- Each day, Diep cuts 15 centimeters of bread for his sandwich.
2. Set Up the Relationship:
- Let [tex]\( l \)[/tex] represent the length of the bread loaf after [tex]\( d \)[/tex] days.
- Initially, when [tex]\( d = 0 \)[/tex], the length [tex]\( l \)[/tex] is 65 centimeters.
- Each day, Diep reduces the length of the loaf by 15 centimeters.
3. Form the Equation:
- After [tex]\( d \)[/tex] days, the new length of the bread, [tex]\( l \)[/tex], is calculated by subtracting the total bread used from the initial length.
- Each day, Diep uses [tex]\( 15 \times d \)[/tex] centimeters of bread.
- Thus, the equation relating [tex]\( l \)[/tex] and [tex]\( d \)[/tex] becomes:
[tex]\[
l = 65 - 15d
\][/tex]
4. Determine the Graph Type:
- Since Diep cuts the bread once each day, the length [tex]\( l \)[/tex] only changes at discrete time intervals (each day).
- Therefore, the graph of the equation should be discrete because [tex]\( l \)[/tex] does not change continuously but rather in discrete steps.
Based on this detailed derivation, the appropriate expression and characteristic of the graph are:
[tex]\[
l = 65 - 15d; \text{discrete}
\][/tex]
Among the provided options, the correct one is:
[tex]\[ l = 65 - 15d; \text{discrete} \][/tex]
