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How Can We Write a Linear Equation from a Given Scenario?

To create a linear equation from a given situation, follow these simple steps:

  1. Find the Variables:
    First, figure out what is changing. Choose letters to represent these changes. For example, let xx stand for the number of hours worked, and let yy be the total amount of money earned.

  2. Look at the Relationships:
    Think about how the variables connect. For instance, if you earn £10 for every hour you work, you can write this connection as:

    y=10xy = 10x

  3. Identify Starting Values:
    Sometimes, there is a starting amount (called the y-intercept). If you get a £5 fee before starting work, you would change the equation to:

    y=10x+5y = 10x + 5

  4. Make the Equation:
    Put everything together into a standard format like y=mx+cy = mx + c. Here:

    • mm means the slope (how much the total changes),
    • cc is the y-intercept (the starting amount).
  5. Use a Number Example:
    If you worked for x=2x = 2 hours, plug that into your equation:

    y=10(2)+5=25y = 10(2) + 5 = 25

    So, after working 2 hours, you would earn £25.

  6. Check Your Work:
    Make sure your equation matches the situation. Look at other examples to see if they fit too.

By following these steps, you can easily create a linear equation from different real-life situations!

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How Can We Write a Linear Equation from a Given Scenario?

To create a linear equation from a given situation, follow these simple steps:

  1. Find the Variables:
    First, figure out what is changing. Choose letters to represent these changes. For example, let xx stand for the number of hours worked, and let yy be the total amount of money earned.

  2. Look at the Relationships:
    Think about how the variables connect. For instance, if you earn £10 for every hour you work, you can write this connection as:

    y=10xy = 10x

  3. Identify Starting Values:
    Sometimes, there is a starting amount (called the y-intercept). If you get a £5 fee before starting work, you would change the equation to:

    y=10x+5y = 10x + 5

  4. Make the Equation:
    Put everything together into a standard format like y=mx+cy = mx + c. Here:

    • mm means the slope (how much the total changes),
    • cc is the y-intercept (the starting amount).
  5. Use a Number Example:
    If you worked for x=2x = 2 hours, plug that into your equation:

    y=10(2)+5=25y = 10(2) + 5 = 25

    So, after working 2 hours, you would earn £25.

  6. Check Your Work:
    Make sure your equation matches the situation. Look at other examples to see if they fit too.

By following these steps, you can easily create a linear equation from different real-life situations!

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