To find the slope of the line passing through the points \((-3, 3)\) and \((5, 9)\), we use the slope formula:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points. In our case:
[tex]\[
x_1 = -3, \, y_1 = 3, \, x_2 = 5, \, y_2 = 9
\][/tex]
Substituting these values into the slope formula, we get:
[tex]\[
\text{slope} = \frac{9 - 3}{5 - (-3)}
\][/tex]
First, calculate the difference in the y-coordinates \( (y_2 - y_1) \):
[tex]\[
9 - 3 = 6
\][/tex]
Next, calculate the difference in the x-coordinates \( (x_2 - x_1) \):
[tex]\[
5 - (-3) = 5 + 3 = 8
\][/tex]
Now, divide the difference in the y-coordinates by the difference in the x-coordinates:
[tex]\[
\text{slope} = \frac{6}{8} = \frac{3}{4}
\][/tex]
Thus, the slope of the line passing through the points \((-3, 3)\) and \((5, 9)\) is:
[tex]\[
\boxed{0.75}
\][/tex]
