choose the graphs that show a linear function

Guri Bee

11 min read

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20-10-2024

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Identifying Linear Functions: A Guide to Recognizing Straight Lines

Linear functions are a fundamental concept in mathematics, describing relationships where the change in one variable is directly proportional to the change in another. Recognizing linear functions visually is crucial for understanding their behavior and applications.

What Makes a Graph Linear?

The key characteristic of a linear function's graph is its straight line shape. This means:

• Constant Slope: The line maintains a consistent "steepness" or incline throughout its length. This slope represents the rate of change between the variables.
• No Curvature: The line does not bend or curve in any direction.

Identifying Linear Functions from Graphs:

Here's a breakdown of methods to identify linear functions from graphical representations:

1. The Straight Line Test:

   • Look for a consistent straight line: The graph should not have any curves, bends, or breaks.
   • Example: [Image of a straight line graph](https://www.google.com/search?q=linear+function+graph&tbm=isch&ved=2ahUKEwiY89G-qLLvAhW1kQIHHfK2D68Q2-cCegQIABAA&oq=linear+function+graph&gs_lcp=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&sclient=img&ei=X6mAYp30B4K1gAbT_aH4Ag&bih=657&biw=1366&hl=en&site=https://www.google.com/search?q=linear+function+graph&tbm=isch&ved=2ahUKEwiY89G-qLLvAhW1kQIHHfK2D68Q2-cCegQIABAA&oq=linear+function+graph&gs_lcp=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&sclient=img&ei=X6mAYp30B4K1gAbT_aH4Ag&bih=657&biw=1366&hl=en&site=https://www.google.com/search?q=linear+function+graph&tbm=isch&ved=2ahUKEwiY89G-qLLvAhW1kQIHHfK2D68Q2-cCegQIABAA&oq=linear+function+graph&gs_lcp=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&sclient=img&ei=X6mAYp30B4K1gAbT_aH4Ag&bih=657&biw=1366&hl=en&site=https://www.google.com/search?q=linear+function+graph&tbm=isch&ved=2ahUKEwiY89G-qLLvAhW1kQIHHfK2D68Q2-cCegQIABAA&oq=linear+function+graph&gs_lcp=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&sclient=img&ei=X6mAYp30B4K1gAbT_aH4Ag&bih=657&biw=1366&hl=en&site=https://www.google.com/search?q=linear+function+graph&tbm=isch&ved=2ahUKEwiY89G-qLLvAhW1kQIHHfK2D68Q2-cCegQIABAA&oq=linear+function+graph&gs_lcp=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&sclient=img&ei=X6mAYp30B4K1gAbT_aH4Ag&bih=657&biw=1366&hl=en
   • Example: [Image of a non-linear graph](https://www.google.com/search?q=non+linear+function+graph&tbm=isch&ved=2ahUKEwiY89G-qLLvAhW1kQIHHfK2D68Q2-cCegQIABAA&oq=non+linear+function+graph&gs_lcp=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&sclient=img&ei=X6mAYp30B4K1gAbT_aH4Ag&bih=657&biw=1366&hl=en&site=https://www.google.com/search?q=non+linear+function+graph&tbm=isch&ved=2ahUKEwiY89G-qLLvAhW1kQIHHfK2D68Q2-cCegQIABAA&oq=non+linear+function+graph&gs_lcp=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&sclient=img&ei=X6mAYp30B4K1gAbT_aH4Ag&bih=657&biw=1366&hl=en&site=https://www.google.com/search?q=non+linear+function+graph&tbm=isch&ved=2ahUKEwiY89G-qLLvAhW1kQIHHfK2D68Q2-cCegQIABAA&oq=non+linear+function+graph&gs_lcp=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&sclient=img&ei=X6mAYp30B4K1gAbT_aH4Ag&bih=657&biw=1366&hl=en&site=https://www.google.com/search?q=non+linear+function+graph&tbm=isch&ved=2ahUKEwiY89G-qLLvAhW1kQIHHfK2D68Q2-cCegQIABAA&oq=non+linear+function+graph&gs_lcp=CgNpbWcQAzIFCAAQgAQyBQgAEIAEMgUIABCABDIFCAAQgAQyBQgAEIAEMgUIABCABDIFCAAQgAQyBQgAEIAEMgUIABCABDoECAAQQzoGCAAQHhANOgQIABAeOgQIABAeOgUIABAKOgYIABAIEB46BwgAELEDEEM6CAgAEIAEELEDOgQIABAeOgYIABAIEB46CAgAEIAEELEDOgQIABAeOgYIABAIEB46BAgAEApQBAoECAAQAzoICAAQgAQQsQM6BQgAEIAEOgQIABAeOgQIABAeOgUIABAKOgYIABAIEB46BwgAELEDEEM6CAgAEIAEELEDOgQIABAeOgYIABAIEB46CAgAEIAEELEDOgQIABAeOgYIABAIEB46BAgAEApQBAoECAAQAzoICA&sclient=img&ei=X6mAYp30B4K1gAbT_aH4Ag&bih=657&biw=1366&hl=en

2. The Slope Calculation:

   • Pick two points on the line: Use the coordinates of these points to calculate the slope.
   • Slope formula: (y2 - y1) / (x2 - x1)
   • Consistent Slope: The slope should be the same regardless of which two points you choose.

Practical Examples:

• Distance vs. Time: A car traveling at a constant speed will have a linear relationship between distance traveled and time elapsed. The graph would be a straight line.
• Cost vs. Quantity: Buying items at a fixed price per unit results in a linear relationship between the total cost and the number of units purchased. The graph would be a straight line.

Key Takeaways:

• Linear functions are characterized by straight-line graphs with a constant slope.
• Identifying linear functions visually allows you to understand and interpret the relationship between variables.
• Be mindful of curves, bends, and breaks in the graph, as they indicate non-linear functions.

Further Exploration:

• Explore how the slope of a linear function relates to its equation (y = mx + c).
• Learn about the different ways to represent linear functions, including equations, tables, and word problems.
• Investigate real-world applications of linear functions in various fields, such as economics, physics, and engineering.