We have to write the point-slope equation of the line.
The point is (4,-2) and the slope has to be calculated.
We need another point to calculate the slope. We see that the y-intercept is y = 6, so another point of the line is (0, 6).
We then can calculate the slope with the points (0,6) and (4,-2):
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-2-6}{4-0} \\ m=-\frac{8}{4} \\ m=-2 \end{gathered}[/tex]
Now that we have the slope m = -2 and the point (4,-2), we can write the equation as:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-(-2)=-2(x-4) \\ y+2=-2(x-4) \end{gathered}[/tex]
Answer: y + 2 = -2(x - 4)
