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Use the coordinates of the plotted points to complete the calculation below. Pay attention to negative signs.

On a coordinate plane, a line goes through (2, 2) and (4, 1).
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change in



Slope


change in

1 answer

To calculate the slope of the line that goes through the points (2, 2) and (4, 1), we can use the formula for slope \( m \):

\[ m = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1} \]

Here, we can represent our points as \( (x_1, y_1) = (2, 2) \) and \( (x_2, y_2) = (4, 1) \).

Now we will substitute the values into the formula:

  1. Change in \( y \) (which is \( y_2 - y_1 \)): \[ y_2 - y_1 = 1 - 2 = -1 \]

  2. Change in \( x \) (which is \( x_2 - x_1 \)): \[ x_2 - x_1 = 4 - 2 = 2 \]

Now, we can substitute these changes into the slope formula:

\[ m = \frac{-1}{2} \]

So the slope of the line is:

\[ \text{slope} = -\frac{1}{2} \]

To summarize:

  • Change in \( y \): \( -1 \)
  • Change in \( x \): \( 2 \)
  • Slope: \( -\frac{1}{2} \)