Answer :
To find the slope of the line containing the two points [tex]\((9, -9)\)[/tex] and [tex]\((-6, 5)\)[/tex], we can use the formula for the slope of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], which is:
[tex]\[
\text{Slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Now, let's plug in the coordinates from the two points into the formula:
- [tex]\(x_1 = 9\)[/tex], [tex]\(y_1 = -9\)[/tex]
- [tex]\(x_2 = -6\)[/tex], [tex]\(y_2 = 5\)[/tex]
Substitute these values into the slope formula:
[tex]\[
\text{Slope} = \frac{5 - (-9)}{-6 - 9}
\][/tex]
Simplify the expression:
1. Calculate the difference in the [tex]\(y\)[/tex]-coordinates: [tex]\(5 - (-9) = 5 + 9 = 14\)[/tex].
2. Calculate the difference in the [tex]\(x\)[/tex]-coordinates: [tex]\(-6 - 9 = -15\)[/tex].
Now, substitute these differences back into the formula:
[tex]\[
\text{Slope} = \frac{14}{-15} = -\frac{14}{15}
\][/tex]
So, the slope of the line containing the two points is [tex]\(-\frac{14}{15}\)[/tex]. Therefore, the correct answer is option C.
[tex]\[
\text{Slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Now, let's plug in the coordinates from the two points into the formula:
- [tex]\(x_1 = 9\)[/tex], [tex]\(y_1 = -9\)[/tex]
- [tex]\(x_2 = -6\)[/tex], [tex]\(y_2 = 5\)[/tex]
Substitute these values into the slope formula:
[tex]\[
\text{Slope} = \frac{5 - (-9)}{-6 - 9}
\][/tex]
Simplify the expression:
1. Calculate the difference in the [tex]\(y\)[/tex]-coordinates: [tex]\(5 - (-9) = 5 + 9 = 14\)[/tex].
2. Calculate the difference in the [tex]\(x\)[/tex]-coordinates: [tex]\(-6 - 9 = -15\)[/tex].
Now, substitute these differences back into the formula:
[tex]\[
\text{Slope} = \frac{14}{-15} = -\frac{14}{15}
\][/tex]
So, the slope of the line containing the two points is [tex]\(-\frac{14}{15}\)[/tex]. Therefore, the correct answer is option C.
