the
Under the assumption that each line on the graph represents 1 unit on both axes.
Step-1: Determine the coordinates of 2 points on the graph
A(-2,1) and B(5,-6)
Step2: Find the slope of the line.
By formula,
[tex]\begin{gathered} \text{Slope = }\frac{y_2-y_1}{x_2-x_1} \\ \text{Where (-2,1)}\Rightarrow x_1=-2;y_1=1 \\ (5,6)\Rightarrow x_2=5;y_2=-6 \end{gathered}[/tex][tex]\text{Slope =}\frac{-6-1}{5--2}=-\frac{7}{7}=-1[/tex]Step 3: Find the equation of the line using the formula below:
[tex]\begin{gathered} y-y_1=slope(x-x_1) \\ \text{Where x}_1=-2;y_1=1 \\ \text{Substituting these values into the formula, we get} \\ y-1=-1(x--2) \\ \text{Simplifying, we get,} \\ y-1=-1(x+2) \\ \text{Clearing the bracket, we get} \\ y-1=-x-2 \\ \text{Collecting like terms, we get} \\ y=-x-2+1 \\ y=-x-1 \end{gathered}[/tex]Hence, the correct answer for equation of the line is y = -x -1
