Question

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).
Clear Check


change in



Slope


change in

Answer 1

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: \( -\frac{1}{2} \)