To find the slope [tex]\( m \)[/tex] of a line that intersects the points [tex]\((2,2)\)[/tex] and [tex]\((-1,20)\)[/tex], we use the slope formula:
[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, [tex]\((2, 2)\)[/tex], and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the second point, [tex]\((-1, 20)\)[/tex].
Let's assign the coordinates to the respective variables:
- [tex]\( x_1 = 2 \)[/tex]
- [tex]\( y_1 = 2 \)[/tex]
- [tex]\( x_2 = -1 \)[/tex]
- [tex]\( y_2 = 20 \)[/tex]
Now, substitute these values into the slope formula:
[tex]\[
m = \frac{20 - 2}{-1 - 2}
\][/tex]
Calculate the difference in the y-coordinates:
[tex]\[
20 - 2 = 18
\][/tex]
Calculate the difference in the x-coordinates:
[tex]\[
-1 - 2 = -3
\][/tex]
Now, substitute these differences back into the slope formula:
[tex]\[
m = \frac{18}{-3}
\][/tex]
Perform the division:
[tex]\[
m = -6
\][/tex]
Thus, the slope of the line in simplest form is:
[tex]\[
m = -6
\][/tex]
