Answer:
[tex]\large\boxed{y=-\dfrac{1}{3}x-\dfrac{10}{3}\to x+3y=-10}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (5, -5) and (-4, -2).
Substiute:
[tex]m=\dfrac{-2-(-5)}{-4-5}=\dfrac{-2+5}{-9}=\dfrac{3}{-9}=-\dfrac{1}{3}[/tex]
Put the value of the slope and the coordinates of the point (5, -5) to the equation of a line:
[tex]-5=-\dfrac{1}{3}(5)+b[/tex]
[tex]-5=-\dfrac{5}{3}+b[/tex] add 5/3 to both sides
[tex]-\dfrac{15}{3}+\dfrac{5}{3}=b\\\\-\dfrac{10}{3}=b\to b=-\dfrac{10}{3}[/tex]
Finally we have the equation of a line in the slope-intercept form:
[tex]y=-\dfrac{1}{3}x-\dfrac{10}{3}[/tex]
Convert to the standard form (Ax + By = C):
[tex]y=-\dfrac{1}{3}x-\dfrac{10}{3}[/tex] multiply both sides by 3
[tex]3y=-x-10[/tex] add x to both sides
[tex]x+3y=-10[/tex]
