The parallel lines have the same slope.
The slope-intercept form: y = mx + b
m - a slope.
We have 6x + y = 4 |subtract 6x from both sides
y = -6x + 4 → m = -6.
The slope-point form:
[tex]y-y_1=m(x-x_1)[/tex]
We have m = -6 and (-2, 3).
Substitute:
[tex]y-3=-6(x-(-2))\\\\y-3=-6(x+2)\\\\y-3=(-6)(x)+(-6)(2)\\\\y-3=-6x-12\qquad|+3\\\\y=-6x-9\qquad|+6x\\\\6x+y=-9[/tex]
Answer: 6x + y = -9.
