The equation of a line is given by
[tex]y=m\cdot x+b[/tex]
Which is the slope-intercept form, where m is the slope and b is the y-intercept
To calculate the slope of the line we need 2 points:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
From the graph we can identify them as A and B
[tex]\begin{gathered} A\to(-4,5) \\ B\to(-2,1) \end{gathered}[/tex]
We replace the points in the equation of the slope:
[tex]\begin{gathered} m=\frac{1-5}{-2-(-4)} \\ m=\frac{-4}{2} \\ m=-2 \end{gathered}[/tex]
Now we replace the value of the slope in the equation of the line:
[tex]y=-2x+b[/tex]
Using any of the 2 points given by the graph (A or B) we will find the b of the equation:
[tex]\begin{gathered} b=y+2x \\ b=5+2(-4) \\ b=5-8 \\ b=-3 \end{gathered}[/tex]
The equation of the line for the graph would be:
[tex]y=-2x-3[/tex]
