To find the slope [tex]\( m \)[/tex] of the line passing through the points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], we'll use the slope formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, the given values are:
- [tex]\( y_2 = 10 \)[/tex]
- [tex]\( y_1 = 1 \)[/tex]
- [tex]\( x_2 = 10 \)[/tex]
- [tex]\( x_1 = 7 \)[/tex]
Let's substitute these values into the formula step-by-step.
1. Calculate the difference in the [tex]\( y \)[/tex]-coordinates ([tex]\( y_2 - y_1 \)[/tex]):
[tex]\[ y_2 - y_1 = 10 - 1 = 9 \][/tex]
2. Calculate the difference in the [tex]\( x \)[/tex]-coordinates ([tex]\( x_2 - x_1 \)[/tex]):
[tex]\[ x_2 - x_1 = 10 - 7 = 3 \][/tex]
3. Divide the difference in [tex]\( y \)[/tex]-coordinates by the difference in [tex]\( x \)[/tex]-coordinates:
[tex]\[ m = \frac{9}{3} = 3.0 \][/tex]
Thus, the slope [tex]\( m \)[/tex] is [tex]\( 3.0 \)[/tex], the difference in [tex]\( y \)[/tex]-coordinates ([tex]\( y_2 - y_1 \)[/tex]) is [tex]\( 9 \)[/tex], and the difference in [tex]\( x \)[/tex]-coordinates ([tex]\( x_2 - x_1 \)[/tex]) is [tex]\( 3 \)[/tex].
So the slope [tex]\( m \)[/tex], and the respective differences are:
[tex]\[ m = 3.0 \][/tex]
[tex]\[ y_2 - y_1 = 9 \][/tex]
[tex]\[ x_2 - x_1 = 3 \][/tex]
