Answer: Pink choice: y= -6x -2
Explanation:
In order to be parallel, the slope must be the same. You find the slope as the number or fraction connected to x. ("co-efficient" of x in math talk)
In the given equation, that is -6. (So that knocks out the first two choices)
The other thing to look at is the y-value of the given coordinate,(-1,4)
(The y-value is the second number in the coordinate (x.y) is the pattern)
and compare it to the the last number in the equations in the choices and Here the Yellow choice has y= -6x + 4 so this line can't pass through the coordinate given, because +4 in this equation is where the line crosses the y-axis. ("y-intercept" in math talk) So yellow choice is out!
The attachment shows what the graphs of the choices look like.
The black line is the correct answer. The given coordinate (-1,4) is the labeled red spot. The blue line is the given equation. (You can see where it "intercepts the y-axis on the +3) And the green line also has the -6 slope, but misses the point and intercepts the y-axis at 4.)
I hope the diagram and explanation helps you understand better. It can be confusing.