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