The equation of a line in slope-intercept form looks like this:
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept. Any point that is part of this line must be a solution wo this equation. Looking at the picture you can see that the line passes through points (-5,1) and (0,-3). Then if we replace x and y in the former equation with the first and second coordinate of each of these points we'll have two equations:
[tex]\begin{gathered} 1=-5m+b \\ -3=m\cdot0+b \end{gathered}[/tex]
By solving these equations we find m and b which means that we'll find the equation requested. First is important to note that the second equation tells us the value of b:
[tex]-3=b[/tex]
If we substitute this value in the first equation we get:
[tex]1=-5m-3[/tex]
Now let's add 3 to both sides of this equation:
[tex]\begin{gathered} 1+3=-5m-3+3 \\ 4=-5m \end{gathered}[/tex]
And we divide both sides by -5:
[tex]\begin{gathered} -\frac{4}{5}=-\frac{5m}{-5} \\ m=-\frac{4}{5} \end{gathered}[/tex]
Now that we have both m and b we have the equation in slope-intercept form:
[tex]y=-\frac{4}{5}x-3[/tex]
Which means that the answer is option A.
