How do you convert the equation 9x + 10y = 9 into slope-intercept form, and what are the slope and y-intercept of this equation?

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To convert the equation 9x + 10y = 9 into slope-intercept form, we need to rearrange it into the format y = mx + b, where m represents the slope, and b represents the y-intercept.

Here are the steps to transform the equation:

  1. Start with the original equation:
    9x + 10y = 9
  2. Isolate the term containing y on one side. To do this, subtract 9x from both sides:
    10y = -9x + 9
  3. Now, divide every term by 10 to solve for y:
    y = -\frac{9}{10}x + \frac{9}{10}

Now, the equation is in slope-intercept form:

y = -\frac{9}{10}x + \frac{9}{10}

From this equation, we can identify the following:

  • Slope (m): -\frac{9}{10}
  • Y-intercept (b): \frac{9}{10}

Thus, the slope of the line is -\frac{9}{10}, indicating that the line falls steeply as it moves from left to right, and the y-intercept is \frac{9}{10}, which is the point where the line crosses the y-axis.

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