Answer:
[tex]\large\boxed{y=-\dfrac{2}{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
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
===============================================
We have the points (2, -1) and (5, -3). Substitute:
[tex]m=\dfrac{-3-(-1)}{5-2}=\dfrac{-2}{3}=-\dfrac{2}{3}[/tex]
We have the equation:
[tex]y=-\dfrac{2}{3}x+b[/tex]
Put the coordinates of the point (2, -1):
[tex]-1=-\dfrac{2}{3}(2)+b[/tex]
[tex]-1=-\dfrac{4}{3}+b[/tex] add 4/3 to both sides
[tex]\dfrac{1}{3}=b\to b=\dfrac{1}{3}[/tex]
Finally:
[tex]y=-\dfrac{2}{3}x+\dfrac{1}{3}[/tex]
