How do you find the slope and y-intercept of the line given by the equation ax + by = 0?

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To find the slope and y-intercept of the line represented by the equation ax + by = 0, you’ll want to rearrange this equation into the slope-intercept form, which is y = mx + b. Here, m represents the slope, and b is the y-intercept.

Follow these steps:

  1. Start with the original equation:

    2. ax + by = 0

  2. Isolate y on one side: Subtract ax from both sides:

    3. by = -ax

  3. Divide every term by b: This will help express y in terms of x:

    4. y = –(a/b)x

Now that we have the equation in slope-intercept form, we can identify the slope and y-intercept:

  • Slope (m): The coefficient of x in the equation, which is –(a/b).
  • Y-intercept (b): The value of y when x = 0. Substituting x with 0 in the rearranged equation gives:

    • When x = 0, y = 0 (since -a(0) / b = 0) thus y-intercept is 0.

In summary:

  • The slope of the line is -a/b.
  • The y-intercept of the line is 0, indicating that the line passes through the origin.

By following these steps, you will effectively determine both the slope and y-intercept of the line!

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