Given the line graphed, you can identify that it passes through this point:
[tex](0,2)[/tex]
The Point-Slope Form of the equation of a line is:
[tex]y-y_1=m(x-y_1)[/tex]
Where "m" is the slope of the line and this is a point on the line:
[tex](x_1,y_1)[/tex]
The Slope-Intercept Form of the equation of a line is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
You can find the slope of the line using this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where these two points are on the line:
[tex](x_1,y_1),(x_2,y_2)[/tex]
In this case, all the answer choices show that the slope is:
[tex]m=-3[/tex]
Then, you can substitute a point on the line graph into the equations provided in the answer choices and evaluate, until you find a true equation:
Using the equation given in Option A, you can substitute:
[tex]\begin{gathered} x=0 \\ y=2 \end{gathered}[/tex]
You get:
[tex]y+1=-3(x-1)[/tex][tex]2+1=-3(0-1)[/tex][tex]3=-3(-1)[/tex][tex]3=3\text{ \lparen True\rparen}[/tex]
Hence, the answer is: Option A.
