To find the slope of the line that passes through the points [tex]\((-2, 2)\)[/tex] and [tex]\((-4, -1)\)[/tex], we need to use the slope formula. The slope [tex]\(m\)[/tex] of a line passing through points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Let's identify our points:
- [tex]\((x_1, y_1) = (-2, 2)\)[/tex]
- [tex]\((x_2, y_2) = (-4, -1)\)[/tex]
Now, we substitute these values into the slope formula:
[tex]\[
m = \frac{-1 - 2}{-4 - (-2)}
\][/tex]
Simplify the numerator and the denominator:
[tex]\[
m = \frac{-1 - 2}{-4 + 2}
\][/tex]
[tex]\[
m = \frac{-3}{-2}
\][/tex]
Since both the numerator and the denominator are negative, the negatives cancel out, leaving:
[tex]\[
m = \frac{3}{2}
\][/tex]
Therefore, the slope of the line that passes through the points [tex]\((-2, 2)\)[/tex] and [tex]\((-4, -1)\)[/tex] is:
[tex]\[
1.5
\][/tex]
