Given (2, 9) and (3, 2), find the slope.

Question image

Understand the Problem

The question is asking to find the slope between two given points, (2, 9) and (3, 2). The slope can be calculated using the formula (y2 - y1) / (x2 - x1).

Answer

The slope is $-7$.
Answer for screen readers

The slope between the points (2, 9) and (3, 2) is $-7$.

Steps to Solve

  1. Identify the Points We are given two points:
  • Point 1: $(x_1, y_1) = (2, 9)$
  • Point 2: $(x_2, y_2) = (3, 2)$
  1. Apply the Slope Formula The formula for the slope $m$ between two points is given by:

$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$

Plugging in the coordinates:

$$ m = \frac{2 - 9}{3 - 2} $$

  1. Calculate the Numerator and Denominator Calculating the values in the formula:
  • Numerator: $2 - 9 = -7$
  • Denominator: $3 - 2 = 1$

Now we have:

$$ m = \frac{-7}{1} $$

  1. Finalize the Calculation Thus, the slope $m$ simplifies to:

$$ m = -7 $$

The slope between the points (2, 9) and (3, 2) is $-7$.

More Information

The slope of a line is a measure of its steepness. A negative slope indicates that as the $x$ value increases, the $y$ value decreases, which is the case here.

Tips

  • Forgetting to subtract in the correct order (i.e., mixing up $y_2 - y_1$ and $x_2 - x_1$).
  • Not recognizing that you should put the coordinates into the slope formula properly.

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