Answer:
The slope should be calculated using the formula [tex](7 - 9) / (1 - 3)[/tex] instead of the one that was proposed in the question.
Step-by-step explanation:
The slope of a line in a cartesian plane is the rate at which [tex]y[/tex] changes with respect to [tex]x[/tex].
For this line, the value of [tex]y[/tex] increased (vertically) from [tex]7[/tex] at [tex](1,\, 7)[/tex] to [tex]9[/tex] at [tex](3,\, 9)[/tex] as the value of [tex]x[/tex] increased (horizontally) from [tex]1[/tex] to [tex]3[/tex].
In other words, [tex]y[/tex] changed by [tex](9 - 7)[/tex] while [tex]x[/tex] changed by [tex](3 - 1)[/tex].
The slope of the line (rate at which [tex]y[/tex] changes with respect to [tex]x[/tex]) would be:
[tex]\displaystyle \frac{\text{rise}}{\text{run}} = \frac{(9 - 7)}{(3 - 1)} = \frac{(7 - 9)}{(1 - 3)}[/tex].
In general, for a line that goes through [tex](x_1,\, y_1)[/tex] and [tex](x_2,\, y_2)[/tex], where [tex]x_{1} \ne x_{2}[/tex]:
[tex]\begin{aligned}\text{slope}&= \frac{(y_1 - y_2)}{(x_1 - x_2)} = \frac{(y_2 - y_1)}{(x_2 - x_1)}\end{aligned}[/tex].
