In a linear model, the constant term gives the output when the input is zero. On a graph, that value is the -intercept, where the line crosses the vertical axis. Check what time zero means in the story, then give the output its units. Don’t mistake the starting amount for the rate of change.
Hints
- Hint 1
An input is the value of . Here, an input of days means no time has passed since the feeder was filled. Which point on the graph has ?
- Hint 2
The -intercept is where the line crosses the vertical axis, so its -coordinate is zero. Read the other coordinate at that point. What does measure?
Step-by-step
Read the starting amount from the graph
Step 1Identify the starting time
No Desmos needed. The given graph already shows the axis crossing. Since counts days after the feeder is filled, is the moment it was filled.
- Step 2
Read the value at day zero
The -intercept is where the line meets the vertical axis, so . The graph shows there. This matches the equation: at , the term is zero, leaving the constant .
- Step 3
Give the number its meaning and units
The constant gives the amount at day , not the amount lost each day. Since measures nectar remaining in milliliters, the feeder initially contains milliliters of nectar. Choice A.