To find the slope of the line passing through the points (-6, 5) and (-3, 20), we need to use the slope formula. The slope of a line between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Given the points [tex]\((-6, 5)\)[/tex] as [tex]\((x_1, y_1)\)[/tex] and [tex]\((-3, 20)\)[/tex] as [tex]\((x_2, y_2)\)[/tex], we can plug these values into the formula step-by-step:
1. Identify the coordinates of the points:
- [tex]\((x_1, y_1) = (-6, 5)\)[/tex]
- [tex]\((x_2, y_2) = (-3, 20)\)[/tex]
2. Substitute these values into the slope formula:
[tex]\[
\text{slope} = \frac{20 - 5}{-3 - (-6)}
\][/tex]
3. Simplify the numerator and the denominator:
- The difference in the y-coordinates (numerator) is:
[tex]\[
20 - 5 = 15
\][/tex]
- The difference in the x-coordinates (denominator) is:
[tex]\[
-3 - (-6) = -3 + 6 = 3
\][/tex]
4. Divide the simplified numerator by the simplified denominator:
[tex]\[
\text{slope} = \frac{15}{3} = 5
\][/tex]
Therefore, the slope of the line that passes through the points (-6, 5) and (-3, 20) is:
[tex]\[
\boxed{5}
\][/tex]
