Solution
Notice that the graph passes through the two points (0,2) and (-2,8)
The equation of the straight line graph will be of the form
[tex]y=mx+c[/tex]Where m is the slope and c is the y - intercept
We will first the slope first
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\begin{gathered} x_1=0 \\ y_1=2_{} \\ x_2=-2 \\ y_2=8 \end{gathered}[/tex][tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{8-2}{-2-0} \\ m=\frac{6}{-2} \\ m=-3 \end{gathered}[/tex]Thus,
[tex]y=-3x+c[/tex]Recall that c is the y - intercept and the y - intercept is at 2
Thus,
[tex]c=2[/tex][tex]y=-3x+2[/tex]We will now consider the options to see which gives the above equation
Option A
[tex]\begin{gathered} y+1=-3(x-1) \\ y+1=-3x+3 \\ y=-3x+3-1 \\ y=-3x+2 \end{gathered}[/tex]Therefore, Option A is Correct