To find the slope of the line passing through the given points, we use the formula for the slope of a line [tex]\(\frac{\Delta y}{\Delta x}\)[/tex], which represents the change in [tex]\(y\)[/tex] over the change in [tex]\(x\)[/tex].
Given points:
[tex]\[
(x_1, y_1) = (15, -10)
\][/tex]
[tex]\[
(x_2, y_2) = (17, 2)
\][/tex]
Now follow these steps:
1. Identify the coordinates of two points.
Point 1: [tex]\((x_1, y_1) = (15, -10)\)[/tex]
Point 2: [tex]\((x_2, y_2) = (17, 2)\)[/tex]
2. Calculate the change in [tex]\(y\)[/tex] ([tex]\(\Delta y\)[/tex]) and the change in [tex]\(x\)[/tex] ([tex]\(\Delta x\)[/tex]).
[tex]\[
\Delta y = y_2 - y_1 = 2 - (-10) = 2 + 10 = 12
\][/tex]
[tex]\[
\Delta x = x_2 - x_1 = 17 - 15 = 2
\][/tex]
3. Use the slope formula [tex]\(\text{slope} = \frac{\Delta y}{\Delta x}\)[/tex].
[tex]\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{12}{2} = 6
\][/tex]
So, the slope of the line that contains the given points is:
[tex]\[
\boxed{6}
\][/tex]
