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Slope equation of the line through (8,-8) and (9,8).

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Final answer:

The slope of the line through the points (8, -8) and (9, 8) is calculated using the slope formula to be 16. This indicates a steep incline since for every unit increase in x, there is a 16 unit rise in y.

Step-by-step explanation:

The student's question pertains to finding the slope equation of a line that passes through the points (8, -8) and (9, 8). To determine the slope, known mathematically as 'm', we use the formula m = (y2 - y1) / (x2 - x1), which represents the change in y-values divided by the change in x-values between two points on a line. In this case:

  1. Substitute the coordinates of the two points into the slope formula to get m = (8 - (-8)) / (9 - 8).
  2. Calculate the difference in y-values and x-values to find m = 16 / 1.
  3. The slope, therefore, equals 16, indicating that for every one unit increase in x, there is a 16 unit increase in y.

This slope is consistent along the entire length of a straight line, just as Figure A1 Slope and the Algebra of Straight Lines suggests that the slope of a line (m) is constant all along the line.

In conclusion, the slope of the line that passes through the points (8, -8) and (9, 8) is 16.

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