Answer:
x + y - 3 = 0
Step-by-step explanation:
The equation of a line when two points are given, it is given by the formula:
[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) $[/tex] are the two points passing through the line.
The two given points are: [tex]$ (x_1,y_1) = (-2,5) $[/tex]
[tex]$ (x_2,y_2) = (5,-2) $[/tex]
Substituting the points in the formula, we get
[tex]$ \frac{y - 5}{-2 -5} = \frac{x + 2}{5 + 2} $[/tex]
[tex]$ \implies \frac{y - 5}{-7} = \frac{x + 2}{7} $[/tex]
[tex]$ \implies y - 5 = -x - 2 $[/tex]
[tex]$ \implies x + y - 3 = 0 $[/tex]
Therefore, the equation of the line passing through the two given points is x + y - 3 = 0.
