How can I determine the equation of the line depicted in this graph?

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To determine the equation of a line depicted in a graph, you typically follow these steps:

  1. Identify Two Points on the Line: Look for two clear points that the line passes through. The coordinates of these points are typically in the format
    (x_1, y_1) and (x_2, y_2).
  2. Calculate the Slope (m): The slope of the line is calculated using the formula:
    m = (y_2 - y_1) / (x_2 - x_1). This gives you the steepness of the line.
  3. Use the Point-Slope Form of the Equation: Once you have the slope, you can use one of the points to formulate the equation. The point-slope form is given by:
    y - y_1 = m(x - x_1).
  4. Rearranging to Slope-Intercept Form: If desired, you can rearrange the equation to the slope-intercept form, y = mx + b, where b is the y-intercept. To find b, substitute one of your points back into the equation after finding m.

For example, if you identify the points (1, 2) and (3, 4), you would calculate the slope:

m = (4 - 2) / (3 - 1) = 2 / 2 = 1

Then, using the point (1, 2):

y - 2 = 1(x - 1)

You can simplify this to find:

y - 2 = x - 1
y = x + 1

Thus, the equation of the line would be y = x + 1.

By following these steps, you’ll be able to accurately find the equation of the line shown in the graph you are analyzing.

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