Answer:
[tex]y = -3x + 6\\[/tex]
Step-by-step explanation:
Find the gradient of the equation
[tex]\frac{Difference in y}{Difference in x} \\\\\frac{6 - - 6}{0 - 4} = \frac{12}{-4} = -3[/tex]
The equation will have the gradient -3x
Use the general equation of a line, and substitute the coordinates in to find the y-intercept.
[tex]y = x + c\\ y = -3x + c\\[/tex]
(4, -6)
[tex]-6 = -3(4) + c\\ -6 = -12 + c\\ -6 + 12 = c\\ c = 6[/tex][tex]6 = -3(0) + c\\ 6 = 0 + c\\ c = 6[/tex]
(0, 6)
[tex]6 = -3(0) + c\\ 6 = -0 + c\\ c = 6[/tex]
The equation of the line is
[tex]y = -3x + 6\\[/tex]
