Let's begin by identifying key information given to us:
[tex](x,y)=(-1,7),(2,-2),(7,-17),(10,-26)[/tex]
We will proceed to calculate the slope, we have:
[tex]\begin{gathered} slope(m)=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ slope(m)=\frac{-26-7}{10-(-1)}=\frac{-33}{10+1}=-\frac{33}{11} \\ slope(m)=-3 \\ \\ The\text{ equation becomes:} \\ y=-3x+b \end{gathered}[/tex]
We will use the point-slope equation to obtain the equation of this data. We have:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ (x_1,y_1)=(-1,7) \\ y-7=-3(x--1) \\ y-7=-3(x+1) \\ y-7=-3x-3 \\ \text{Add ''7'' to both sides, we have:} \\ y-7+7=-3x-3+7 \\ y=-3x+4 \\ \\ \therefore y=-3x+4 \end{gathered}[/tex]
Hence, the correct answer is y = -3x + 4
