Answer:
[tex]\large\boxed{y=-\dfrac{1}{3}x+\dfrac{10}{3}}[/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 two points (-5, 5) and (4, 2).
substitute:
[tex]m=\dfrac{2-5}{4-(-5)}=\dfrac{-3}{9}=-\dfrac{1}{3}[/tex]
Put the value os a slope and coordinates of the point (4, 2) to the equation of a line:
[tex]2=-\dfrac{1}{3}(4)+b[/tex]
[tex]2=-\dfrac{4}{3}+b[/tex] add 4/3 to both sides
[tex]2\dfrac{4}{3}=b\to b=3\dfrac{1}{3}\to b=\dfrac{10}{3}[/tex]
