To find the slope of the line passing through the points [tex]\((8, 3)\)[/tex] and [tex]\((6, 9)\)[/tex], we use the slope formula. The slope formula is given by:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, [tex]\((x_1, y_1)\)[/tex] are the coordinates of the first point [tex]\((8, 3)\)[/tex], and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the second point [tex]\((6, 9)\)[/tex].
Substitute the coordinates into the formula:
[tex]\[ \text{slope} = \frac{9 - 3}{6 - 8} \][/tex]
First, we calculate the difference in the y-coordinates [tex]\((y_2 - y_1)\)[/tex]:
[tex]\[ 9 - 3 = 6 \][/tex]
Next, we calculate the difference in the x-coordinates [tex]\((x_2 - x_1)\)[/tex]:
[tex]\[ 6 - 8 = -2 \][/tex]
So, our expression for the slope now looks like:
[tex]\[ \text{slope} = \frac{6}{-2} \][/tex]
Finally, we perform the division:
[tex]\[ \frac{6}{-2} = -3.0 \][/tex]
Therefore, the slope of the line through [tex]\((8, 3)\)[/tex] and [tex]\((6, 9)\)[/tex] is [tex]\(\boxed{-3.0}\)[/tex].
