Answer:
5x + y - 4 = 0
Step-by-step explanation:
When we are given two points and are asked to find the equation of the line we use the two - point form.
Two - point form: [tex]$ \frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1} $[/tex].
where: [tex]$ (x_1,y_1) $[/tex] and [tex]$ (x_2,y_2) $[/tex] are the two points on the line.
Given the two points are: (5,21) and (-5,-29).
Substituting in the two point form:
⇒ [tex]$ \frac{y - 21}{-29 - 21} = \frac{x - 5}{-5 -5} $[/tex]
[tex]$ \implies \frac{y - 21}{-50} = \frac{x - 5}{-10} $[/tex]
[tex]$ \implies y - 21 = 5x - 25 $[/tex]
⇒ 5x + y - 4 = 0
