Hi there!
Looking at the answer choices, it seems that the question is asking for the equation in point-slope form. Point slope is usually used when you are given a slope and a coordinate. The point slope formula is:
[tex]y-y_1=m(x-x_1)[/tex]
x and y remain constant they DO NOT change. Do not confuse this with y1 and x1. x1 and y1 are values given to you in the coordinate that is provided by the question. (-6,1) -> (x1,y1)
x1=-6
y1=1
The question also gives us the slope (1/4). In the point slope formula m=slope.
Review:
We are given the slope (m=1/4) the x1 value (-6) and y1 value (1), now we can plug these values into the point slope formula:
[tex]y-1=1/4(x-(-6))[/tex]
Note: Remember that when there are 2 "-" signs next to each other they become a "+" sign.
[tex]y-1=1/4(x+6)[/tex]
Therefore, our final answer is:
[tex]y-1=1/4(x+6)[/tex]
C (The third option)
