Answer:
[tex]\large\boxed{y=-\dfrac{2}{3}x-\dfrac{13}{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]
From the graph we have two points (-5, -1) and (-2, -3).
Look at the picture.
Calculate the slope:
[tex]m=\dfrac{-3-(-1)}{-2-(-5)}=\dfrac{-2}{3}=-\dfrac{2}{3}[/tex]
Put it to the equation in slope-intercept form:
[tex]y=-\dfrac{2}{3}x+b[/tex]
We can't read the y-intercept from the graph. Therefore put the coordinates of the point (-5, -1) to the equation and calculate b:
[tex]-1=-\dfrac{2}{3}(-5)+b[/tex]
[tex]-1=\dfrac{10}{3}+b[/tex] subtract 10/3 from both sides
[tex]-\dfrac{3}{3}-\dfrac{10}{3}=b\to b=-\dfrac{13}{3}[/tex]
Finally:
[tex]y=-\dfrac{2}{3}x-\dfrac{13}{3}[/tex]
