To find the slope [tex]\( m \)[/tex] of the line that intersects the points [tex]\((8, 2)\)[/tex] and [tex]\((12, -10)\)[/tex], we need to use the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, the coordinates of the points are:
- Point 1: [tex]\((x_1, y_1) = (8, 2)\)[/tex]
- Point 2: [tex]\((x_2, y_2) = (12, -10)\)[/tex]
First, calculate the difference in the y-coordinates ([tex]\( y_2 - y_1 \)[/tex]):
[tex]\[
y_2 - y_1 = -10 - 2 = -12
\][/tex]
Next, calculate the difference in the x-coordinates ([tex]\( x_2 - x_1 \)[/tex]):
[tex]\[
x_2 - x_1 = 12 - 8 = 4
\][/tex]
Now, substitute these differences into the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-12}{4}
\][/tex]
Simplify the fraction:
[tex]\[
m = \frac{-12}{4} = -3
\][/tex]
Therefore, the slope of the line in simplest form is:
[tex]\[
m = -3
\][/tex]
