https://file.aiquickdraw.com/mathbot/file/1726782305803ou8fu9yx.jpg

The graphs of two linear equations are shown above. The graph of 𝑦=𝑓(𝑥)
 is in green and the graph of 𝑦=𝑔(𝑥)
 is in blue. Find the interval where 𝑓(𝑥)≥𝑔(𝑥)
. Write your answer in interval notation or as an inequality. For example, if you think that the solution is 𝑥<=−7
, you would this or enter (−𝑖𝑛𝑓,−7]


To find the interval where \( f(x) \geq g(x) \), let's analyze the graph and focus on the intersection and behavior of the two functions.

1. **Intersection point**: The graphs of \( f(x) \) (green) and \( g(x) \) (blue) intersect at approximately \( (x = 1, y = 2) \). This is the point where \( f(x) = g(x) \).

2. **Behavior of the functions**:
   - **To the left of the intersection point** (for \( x < 1 \)): The green line (representing \( f(x) \)) is **above** the blue line (representing \( g(x) \)). Hence, \( f(x) > g(x) \).
   - **To the right of the intersection point** (for \( x > 1 \)): The green line is **below** the blue line, meaning \( f(x) < g(x) \).

Thus, the interval where \( f(x) \geq g(x) \) occurs when \( x \leq 1 \), including the point where they intersect.

### Final Answer:
The solution is \( (-\infty, 1] \).

Would you like more details on how to interpret the graph or solve this? 

Here are five questions to expand this concept:

1. How do you find the intersection points of two linear equations algebraically?
2. How can you determine the slopes of linear functions from a graph?
3. What does it mean when one function is above another on a graph?
4. How do you express inequalities in interval notation?
5. What role does the intersection point play in solving inequalities involving two functions?

**Tip**: When working with graphs of functions, always focus on key points like intersections and the behavior of the functions on either side of these points.

The graphs of two linear equations are shown above. The graph of y = f(x) is in green and the graph of y = g(x) is in blue. Find the interval where f(x) ≥ g(x). Write your answer in interval notation or as an inequality. For example, if you think that the solution is x <= −7, you would this or enter (−∞,−7].

Find the interval where f(x) is greater than or equal to g(x) using the graphs of two linear equations. This problem covers key algebraic concepts, including linear equations, graph analysis, and solving inequalities. Suitable for students in Grades 8-10.

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