To find the slope of the line passing through the points [tex]\((9, -4)\)[/tex] and [tex]\((3, -9)\)[/tex], we will use the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, [tex]\((x_1, y_1) = (9, -4)\)[/tex] and [tex]\((x_2, y_2) = (3, -9)\)[/tex].
Step-by-step solution:
1. Identify the coordinates of the two points:
- First point [tex]\((x_1, y_1) = (9, -4)\)[/tex]
- Second point [tex]\((x_2, y_2) = (3, -9)\)[/tex]
2. Substitute the coordinates into the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
3. Calculate the differences in the y-values and x-values:
- [tex]\(y_2 - y_1 = -9 - (-4) = -9 + 4 = -5\)[/tex]
- [tex]\(x_2 - x_1 = 3 - 9 = -6\)[/tex]
4. Substitute these values back into the slope formula:
[tex]\[
m = \frac{-5}{-6}
\][/tex]
5. Simplify the fraction:
[tex]\[
m = \frac{5}{6}
\][/tex]
Thus, the slope of the line passing through the points [tex]\((9, -4)\)[/tex] and [tex]\((3, -9)\)[/tex] is [tex]\(\frac{5}{6}\)[/tex].
So, the correct numerical representation in decimal form is:
[tex]\[
m = 0.8333333333333334
\][/tex]
Therefore, the slope of the line passing through the given points is [tex]\(\boxed{0.8333333333333334}\)[/tex].
