To find the slope of the line that passes through the points [tex]\((2, 9)\)[/tex] and [tex]\((18, -3)\)[/tex], we can use the slope formula. The slope (m) of a line passing through two 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 break it down step by step by substituting the given points into the formula:
1. Identify the coordinates of the two points.
- Point 1: [tex]\((x_1, y_1) = (2, 9)\)[/tex]
- Point 2: [tex]\((x_2, y_2) = (18, -3)\)[/tex]
2. Calculate the change in y (Δy) and the change in x (Δx).
- Δy = [tex]\(y_2 - y_1\)[/tex]
- Δx = [tex]\(x_2 - x_1\)[/tex]
Substitute the values from the points:
- Δy = [tex]\(-3 - 9 = -12\)[/tex]
- Δx = [tex]\(18 - 2 = 16\)[/tex]
3. Substitute Δy and Δx into the slope formula:
[tex]\[ m = \frac{\Delta y}{\Delta x} = \frac{-12}{16} \][/tex]
4. Simplify the fraction:
[tex]\[ \frac{-12}{16} = -0.75 \][/tex]
Therefore, the slope of the line that passes through the points [tex]\((2, 9)\)[/tex] and [tex]\((18, -3)\)[/tex] is [tex]\(-0.75\)[/tex].
