Hi Emily,
In order to write the equation of a specific line, we generally need two things: the slope (m) and the y-intercept (b). Once we have those two things, we can write the equation as y = mx + b.
Fortunately, the problem gives us the y-intercept: b= -2
All we need is the slope. We are told that the line we are looking for is perpendicular to the line y = 4x + 6. This line has a slope of m = 4. The slope of a perpendicular line to this line is the negative reciprocal of 4 which is -1/4.
Therefore, the equation of the line we are looking for is y = (-1/4)x - 2
Hope this helps!
:)
