Question

What is the equation of the line in standard form that passes through the point (3, –2) and is parallel to the line y = –4x + 1?


A. 4x – y = –10
B. 4x + y = 10
C. x + 4y = 10
D. x – 4y = –10

Answer 1

Hi there. Okay...
So if a line is parallel to another, it has the same slope as the other line.
In y = mx + b, m is the slope
So, in y = -4x + 1, -4 is the slope
So -4 is the slope of the linear equation you are trying to find
Next, we plug in 3 for x and -2 for y to find b, the y-intercept
-2 = -4*3 + b; b = -2 + 12 = 10
So...using y = mx + b again, and our values for m and b, we get that y = -4x + 10.
Rearrange terms: 4x + y = 10.

So the answer is B.

If you feel you need to understand this better, or it is possible for you to solve this problem through a variety of methods, you could alternatively graph all four answers they give to visually demonstrate to yourself what I have explained above.

Hope this helps.

Answer 2

If you are to graph them, make sure to graph them against the original linear equation, so that you can see the relationship between answer B and our original line parallel to it!