To find the equation in slope-intercept form, we shall begin by finding the slope of the line.
First step is to identify two different points on the line. Observe carefully that when x equals 0, y equals 2. Therefore we have (0, 2). Also when x equals 2, y equals negative 6. Therefore, the other point is (2, -6). With these two points we can now calculate the slope as follows;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ (x_1,y_1)\rightarrow(0,2) \\ (x_2,y_2)\rightarrow(2,-6) \\ m=\frac{-6-2}{2-0} \\ m=-\frac{8}{2} \\ m=-4 \end{gathered}[/tex]
With the slope derived as -4, we can now determine the value of b (the y-intercept). We shall take any of the points above, hence let use the first point;
[tex]\begin{gathered} y=mx+b \\ 2=-4(0)+b \\ 2=0+b \\ 2=b \\ y=mx+b\text{ now becomes} \\ y=-4x+2 \end{gathered}[/tex]
The equation therefore is y = -4x + 2
