Hello!
Point-slope form is this: [tex]y - y_{1} = m(x - x_{1})[/tex]. In this form, m is the slope, [tex]x_{1}[/tex] and [tex]y_{1}[/tex] is an ordered pair, or point.
To find the slope, we need to use the slope formula. The slope formula is: [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. We can assign the point (-9, 6) to [tex]x_{1}[/tex] and [tex]y_{1}[/tex] and (-7, -8) to [tex]x_{2}[/tex] and [tex]y_{2}[/tex].
Now, we can substitute the ordered pairs into the formula and solve.
[tex]m = \frac{-8 - 6}{-7 - (-9)} = \frac{-14}{2} = -7[/tex]
Since the slope is equal to -7, we can substitute the slope and a point into the point-slope form.
Therefore, your point-slope formula is y - 6 + -7(x + 9) or y + 8 = -7(x + 7).
