To find the slope of the line that passes through the points [tex]\((9, -10)\)[/tex] and [tex]\((14, 5)\)[/tex], we will use the slope formula. The slope [tex]\( m \)[/tex] between 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]
Here, the coordinates of our points are:
- [tex]\((x_1, y_1) = (9, -10)\)[/tex]
- [tex]\((x_2, y_2) = (14, 5)\)[/tex]
Now, let's plug these values into the slope formula:
[tex]\[
m = \frac{5 - (-10)}{14 - 9}
\][/tex]
First, simplify the numerator:
[tex]\[
5 - (-10) = 5 + 10 = 15
\][/tex]
Next, simplify the denominator:
[tex]\[
14 - 9 = 5
\][/tex]
Thus, our slope calculation becomes:
[tex]\[
m = \frac{15}{5}
\][/tex]
Finally, simplify the fraction:
[tex]\[
m = 3
\][/tex]
Therefore, the slope of the line that passes through the points [tex]\((9, -10)\)[/tex] and [tex]\((14, 5)\)[/tex] is [tex]\(\boxed{3.0}\)[/tex].
