Question
A new community center opened in 2015 with an initial membership of 800 people. The number of members, y
, grows as a linear function of time, x
, where x
represents the number of years since 2015. By 2021, the membership had increased to 1,400 people. Sketch a graph of the situation. Where would you place the y-intercept?
(1 point)
Responses
(0, 800)
(0, 800)
(800, 0)
(800, 0)
(0, 1400)
(0, 1400)
(1400, 0)
(1400, 0)
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, grows as a linear function of time, x
, where x
represents the number of years since 2015. By 2021, the membership had increased to 1,400 people. Sketch a graph of the situation. Where would you place the y-intercept?
(1 point)
Responses
(0, 800)
(0, 800)
(800, 0)
(800, 0)
(0, 1400)
(0, 1400)
(1400, 0)
(1400, 0)
Skip to navigation
Answers
GPT-4o mini
To approach this problem, we need to analyze the linear growth of membership over time.
1. **Determine the Coordinates**:
- The initial membership in 2015 (which corresponds to \(x = 0\)) was 800 people. Thus, the point is \((0, 800)\).
- By 2021 (which corresponds to \(x = 6\) since 2021 - 2015 = 6), the membership grew to 1,400 people. Thus, the point is \((6, 1400)\).
2. **Finding the y-Intercept**:
- The y-intercept of a function represents the value of \(y\) when \(x = 0\). In this context, since we know the initial membership was 800 in 2015, the y-intercept is at the point \((0, 800)\).
3. **Graph Sketch**:
- You would start your y-axis at zero and plot the two points: \((0, 800)\) and \((6, 1400)\).
- Draw a straight line connecting these two points to depict the linear growth of membership over time.
4. **Conclusion**:
- The correct placement of the y-intercept is: **(0, 800)**.
So, the answer is:
**(0, 800)**
1. **Determine the Coordinates**:
- The initial membership in 2015 (which corresponds to \(x = 0\)) was 800 people. Thus, the point is \((0, 800)\).
- By 2021 (which corresponds to \(x = 6\) since 2021 - 2015 = 6), the membership grew to 1,400 people. Thus, the point is \((6, 1400)\).
2. **Finding the y-Intercept**:
- The y-intercept of a function represents the value of \(y\) when \(x = 0\). In this context, since we know the initial membership was 800 in 2015, the y-intercept is at the point \((0, 800)\).
3. **Graph Sketch**:
- You would start your y-axis at zero and plot the two points: \((0, 800)\) and \((6, 1400)\).
- Draw a straight line connecting these two points to depict the linear growth of membership over time.
4. **Conclusion**:
- The correct placement of the y-intercept is: **(0, 800)**.
So, the answer is:
**(0, 800)**