To find the slope of the line through the points [tex]\((-1, -3)\)[/tex] and [tex]\((-10, 9)\)[/tex], we need to use the slope formula, which is given by:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, [tex]\((x_1, y_1)\)[/tex] are the coordinates of the first point, and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the second point. Identifying the coordinates from the question, we have:
[tex]\[
(x_1, y_1) = (-1, -3)
\][/tex]
[tex]\[
(x_2, y_2) = (-10, 9)
\][/tex]
First, calculate the difference in the [tex]\(y\)[/tex]-coordinates ([tex]\(y_2 - y_1\)[/tex]):
[tex]\[
y_2 - y_1 = 9 - (-3) = 9 + 3 = 12
\][/tex]
Next, calculate the difference in the [tex]\(x\)[/tex]-coordinates ([tex]\(x_2 - x_1\)[/tex]):
[tex]\[
x_2 - x_1 = -10 - (-1) = -10 + 1 = -9
\][/tex]
Now, we can find the slope [tex]\(m\)[/tex] by dividing the difference in [tex]\(y\)[/tex]-coordinates by the difference in [tex]\(x\)[/tex]-coordinates:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{12}{-9} = -\frac{12}{9} = -\frac{4}{3}
\][/tex]
Therefore, the slope of the line through the points [tex]\((-1, -3)\)[/tex] and [tex]\((-10, 9)\)[/tex] is:
[tex]\[
-\frac{4}{3}
\][/tex]
