To complete the point-slope equation of the line passing through the points [tex]\((-9, 6)\)[/tex] and [tex]\((-7, -8)\)[/tex], we need to find the slope of the line and then use the point-slope form of a linear equation.
1. Find the slope: The slope [tex]\( m \)[/tex] of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by the formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Plugging in the given points [tex]\((-9, 6)\)[/tex] and [tex]\((-7, -8)\)[/tex]:
[tex]\[
m = \frac{-8 - 6}{-7 + 9} = \frac{-14}{2} = -7
\][/tex]
2. Use the point-slope form: The point-slope form of a linear equation is:
[tex]\[
y - y_1 = m (x - x_1)
\][/tex]
Here, [tex]\( m = -7 \)[/tex] and the point [tex]\( (x_1, y_1) = (-9, 6) \)[/tex].
Substituting these values into the form:
[tex]\[
y - 6 = -7 (x + 9)
\][/tex]
Thus, the completed point-slope equation of the line through [tex]\((-9, 6)\)[/tex] and [tex]\((-7, -8)\)[/tex] is:
[tex]\[
y - 6 = -7 (x + 9)
\][/tex]
