Answer:
Option (2)
Step-by-step explanation:
Let the equation of the line is,
y - y' = m(x - x')
where (x', y') is a point lying on the given line.
And m = slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Line given in the graph passes through two points (-5, -1) and (-2, -3).
Slope of the line 'm' = [tex]\frac{-3+1}{-2+5}[/tex]
= [tex]-\frac{2}{3}[/tex]
Therefore, equation of the line passing through(-5, -1) and slope of the line = [tex]-\frac{2}{3}[/tex] will be,
y - (-1) = [tex]-\frac{2}{3}[x-(-5)][/tex]
[tex]y+1=-\frac{2}{3}(x+5)[/tex]
[tex]y=-\frac{2}{3}x-\frac{10}{3}-1[/tex]
[tex]y=-\frac{2}{3}x-\frac{13}{3}[/tex]
Option (2) will be the answer.
