Let's begin by listing out the information given to us:
[tex](x,y)=(1,-2),(2,-6),(3,-10),(4,-14)[/tex]The slope-intercept form is given by:
[tex]\begin{gathered} y=mx+b \\ where\colon m=slope,b=y-intercept \end{gathered}[/tex]The slope is calculated by picking any two ordered pairs or coordinates and substituted into the slope formula:
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ (x_1,y_1)=(1,-2);(x_2,y_2)=(4,-14) \\ m=\frac{-14-(-2)}{4-1}=\frac{-14+2}{3}=\frac{-12}{3} \\ m=-4 \end{gathered}[/tex]We proceed to use the point-slope equation to derive this function:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ m=-4 \\ (x_1,y_1)=(1,-2) \\ y-(-2)=-4(x-1) \\ y+2=-4x+4 \\ y=-4x+4-2 \\ y=-4x+2 \\ \\ \therefore y=-4x+2 \end{gathered}[/tex]