Answer:
x + 3y - 16 = 0
Step-by-step explanation:
When two points, say [tex]$ (x_1, y_1) $[/tex] and [tex]$ (x_2, y_2) $[/tex] are given, the equation is determined using Two - point form.
The two - point form is as follows:
[tex]$ \frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1} $[/tex]
Here: [tex]$ (x_1, y_1) = (-6, 7) $[/tex] and [tex]$(x_2, y_2) = (-3, 6) $[/tex].
Substituting in the formula we get the equation of the line as:
[tex]$ \frac{y - 7}{6 - 7} = \frac{x + 6}{- 3 + 6}[/tex]
[tex]$ \implies \frac{y - 7}{- 1} = \frac{x + 6}{ 3} $[/tex]
[tex]$ \implies 3y - 21 = - x - 6 $[/tex]
Rearranging we get: x + 3y - 15 = 0
This is the required equation of the line.
