Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Complete the point-slope equation of the line through [tex]$(-9,6)$[/tex] and [tex]$(-7,-8)$[/tex].
Use exact numbers.

[tex] y - 6 = \boxed{} [/tex]

Sagot :

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]