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How Can You Determine the Slope from a Graph of a Linear Equation?

To find the slope from a graph of a straight line, just follow these simple steps:

  1. Pick Two Points:

    • Find any two points on the line. It’s easier if the points have whole numbers.
  2. Write Down the Points:

    • Let’s call the points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2). For example, if you choose the points (1,2)(1, 2) and (4,5)(4, 5), then you have x1=1x_1 = 1, y1=2y_1 = 2, x2=4x_2 = 4, and y2=5y_2 = 5.
  3. Use the Slope Formula:

    • To find the slope, use this formula:
    m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}
    • Plug in the numbers from our points:
    m=5241=33=1m = \frac{5 - 2}{4 - 1} = \frac{3}{3} = 1
  4. Understand the Slope:

    • A positive slope (like m=1m = 1) means the line goes up as you move to the right.
    • A negative slope means the line goes down.
    • If the slope is zero, the line is flat (horizontal).
    • An undefined slope means the line goes straight up and down (vertical).
  5. Check with Rise Over Run:

    • You can also think of the slope as "rise over run." Here, the rise is how much you go up or down, and the run is how much you go left or right.
    • In our example, for every 3 units you move up (rise), you also move 3 units to the right (run).

By following these steps, you can easily find the slope from the graph of a straight line!

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How Can You Determine the Slope from a Graph of a Linear Equation?

To find the slope from a graph of a straight line, just follow these simple steps:

  1. Pick Two Points:

    • Find any two points on the line. It’s easier if the points have whole numbers.
  2. Write Down the Points:

    • Let’s call the points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2). For example, if you choose the points (1,2)(1, 2) and (4,5)(4, 5), then you have x1=1x_1 = 1, y1=2y_1 = 2, x2=4x_2 = 4, and y2=5y_2 = 5.
  3. Use the Slope Formula:

    • To find the slope, use this formula:
    m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}
    • Plug in the numbers from our points:
    m=5241=33=1m = \frac{5 - 2}{4 - 1} = \frac{3}{3} = 1
  4. Understand the Slope:

    • A positive slope (like m=1m = 1) means the line goes up as you move to the right.
    • A negative slope means the line goes down.
    • If the slope is zero, the line is flat (horizontal).
    • An undefined slope means the line goes straight up and down (vertical).
  5. Check with Rise Over Run:

    • You can also think of the slope as "rise over run." Here, the rise is how much you go up or down, and the run is how much you go left or right.
    • In our example, for every 3 units you move up (rise), you also move 3 units to the right (run).

By following these steps, you can easily find the slope from the graph of a straight line!

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