To find the slope of the line that passes through the points (3, 1) and (2, -3), we will use the slope formula. The slope [tex]\( m \)[/tex] of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] can be calculated using the formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Step-by-step, here's how we apply this formula to our specific points:
1. Identify the coordinates of the points:
- [tex]\((x_1, y_1) = (3, 1)\)[/tex]
- [tex]\((x_2, y_2) = (2, -3)\)[/tex]
2. Substitute these coordinates into the slope formula:
[tex]\[
m = \frac{-3 - 1}{2 - 3}
\][/tex]
3. Compute the differences in the numerator and the denominator:
- Difference in the [tex]\( y \)[/tex]-coordinates: [tex]\(-3 - 1 = -4\)[/tex]
- Difference in the [tex]\( x \)[/tex]-coordinates: [tex]\(2 - 3 = -1\)[/tex]
4. Substitute these differences back into the slope formula:
[tex]\[
m = \frac{-4}{-1}
\][/tex]
5. Simplify the fraction:
[tex]\[
m = 4
\][/tex]
Thus, the slope of the line passing through the points (3, 1) and (2, -3) is [tex]\( 4.0 \)[/tex].
